However, the Monaco chief has revealed that it was Arsenal who nearly secured a deadline day deal for Lemar but the Gunners left it too late to try and get a transfer over the line.
Monaco will also consider selling Fabinho next summer after "strong" interest from Manchester United and Manchester City in the previous window. "You never want to make any major changes in January, except something really extraordinary".
"Liverpool were really interested", Vasilyev told Sky Sports.
'It was quite close. But it was Arsenal that was really close to finalising deal.
Not all the elements of the puzzle fell into place.
Vadim Vasilyev said, "He wanted to go to the Premier League and I had a few discussions with him and I said 'stay, stay, stay" but, of course, when the offers were very, very high, higher than we initially expected then we had to talk, to discuss.
The player in question is Thomas Lemar and both clubs came very close to signing to signing him in the recent window. "He is very important, we can always count on".
"Definitely next summer (it) will be something to look at, although you know in football there are no guarantees".
'We had some players who were supposed to leave this summer but didn't leave because of X, Y, Z. I think it would be fair to say Thomas will have a fair chance to an exit next year.
January is unlikely to be the right time for Fabinho, however, with Monaco hopeful of keeping hold of him until the end of the season.
His performances from midfield attracted the attention of some of the Premier League's top clubs, with both Liverpool and Arsenal making substantial offers in the final hours of the transfer window. "We just have to find the right time for each of them (players)".
A hugely talented prospect with vast potential, Lemar could well be one of the options that Arsenal turn to in order to fill the void left by Mesut Ozil and Alexis Sanchez should their star players, who are in the final year of their contracts, depart the club. "I didn't check but I suspect it's too much for us".
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