Sky Sports News understands the latest offer made by Liverpool was around £64.8m, having previously submitted an offer worth £55.5m.
It is being reported by a number of sources, including the Liverpool Echo, that the Merseyside club have lodged a bid with the French champions as they make a last push to strengthen their squad ahead of Thursdays transfer deadline.
It's not all bad news for Liverpool, however, as they confirmed the signing of RB Leipzig's Naby Keita on Monday night.
The Frenchman said that Arsenal would not be signing Lemar as Monaco have closed the door on any more major outgoings.
With Benjamin Mendy and Bernardo Silva joining City, Tiemoue Bakayoko signing for Chelsea and kid wonder Kylian Mbappe on the verge of making a insane move to Paris Saint-Germain, Monaco are loath to see Lemar depart as well.
Speaking after their 6-3 aggregate win over Hoffenheim last week, Jurgen Klopp said: "It's [Champions League qualification] a big influence on the transfer market, especially if we do it more often".
Rashford maintains Man Utd's winning start
There is no question Leicester City improved down the stretch last season following the arrival of Craig Shakespeare to the bench. James battled his way back to form and fitness with the help of a highly successful loan spell with Barnsley last season.
"I said I think before the game, if you talk to a player, they really often. especially players we talk to".
Lemar has been one of the most attractive targets in Europe this summer, after a fantastic season as part of AS Monaco's title-winning side past year, yet has so far stayed clear of the personnel exodus that has raked in over £300m for the principality club. It also looks like Kylian Mbappe will be joining Paris Saint-Germain so Monaco will not want to lose another key player by letting Lemar join Liverpool.
The promising 21-year-old scored 12 goals in 39 appearances last season and has three years left on his Monaco contract.
And then there's her outsized mezzo-soprano, which is variously described as "raspy", "husky", "soulful" and "prodigious". Who is nominated: With eight nominations , Kendrick Lamar tops the list of VMA nominees .
A whole range of Whole Foods products are about to get cheaper thanks to Amazon's acquisition of Whole Foods Market on August 28. The union, which represents grocery workers, said the deal was "a threat to Whole Foods workers and their families".
The 22-year-old RB Leipzig midfielder has been Jurgen Klopp's top transfer target for the duration of the summer. The Reds have now beaten out Barcelona for Keita's signature after the Spanish side were linked to him last week.
Singh is also under investigation over allegations that he convinced 400 of his male followers to undergo castration. India has been rocked by numerous scandals involving popular ascetics claiming to possess mystical powers.
Tal Afar has produced some of IS's most senior commanders and was cut off from the rest of IS-held territory in June. A security officer flashes the victory gesture during the advance in the eastern part of the town of Tal Afar .
In June, Indian soldiers had crossed the Sikkim border to stop China from constructing a road on the Doklam Plateau in Bhutan . Beijing had accused India of transgressing into its territory and demanded immediate withdrawal of Indian troops.
An earlier assessment by PACOM had said that two missiles failed in flight. "I think it's going to take some time to tell". Kim said he would consider sending missiles into the waters off the coast of Guam in "mid-August".
Lalu's younger son and former deputy chief minister Tejashwi Yadav himself is taking stock of the preparations for the rally. K C Tyagi said that Mr Yadav had participated in a rally organised by RJD without any due permission from the party.
Ram Rahim was finally convicted of rape by the special CBI Court in Panchukla on Friday and faces jail term of upto 7 years. The quantum of sentence for Ram Rahim Singh who was stripped off "Z" category security will be pronounced on August 28.
AsVariety reports, the LA county coroner confirmed that Hooper passed away on Saturday (August 26) in Sherman Oaks, California. It featured a family coping with a house haunted by ghosts and was a box office success.
US Open player profile: Maria Sharapova
Even if she lost my bet in the French Open , I think she had more matches and more consistent this year playing, definitely, yes. Will you, as a fan, watch Simona play Maria? And we'll still be injured because now we're not playing enough.
Game of Thrones season 7 finale
This is a monthly subscription service you can subscribe directly to HBO with, giving you access to every show on the network. With these credentials, you can log in to HBO Go and stream the new episode wherever you wish.
Lebanon finds suspected remains of ISIL-held soldiers
Hezbollah has been fighting alongside troops loyal to President Bashar al-Assad since the Syrian conflict erupted in 2011. In a speech Thursday, the Hezbollah leader Hassan Nasrallah said that Islamic State had been defeated.
When, where to watch PV Sindhu-Nozomi Okuhara final
The two players have met seven times so far in worldwide badminton with Saina having an upper hand in six of those battles. Overpowering the long rallies, the Japanese leveled the lead soon with her strong stamina and won the first game 21-19.