Arsenal saw a series of bids rejected for the France international last summer , and potentially would have signed him on deadline day had Alexis Sanchez's move to Manchester City not fallen through.
The 22-year-old was also the subject of a £70 million offer from Liverpool and continues to be linked with the Reds as Jurgen Klopp aims to find a long-term replacement for Philippe Coutinho following the Brazilian's move to Barcelona.
Lemar admits it was something of a blow not to move to the Premier League but hopes to receive new offers at the end of the season.
Asked if he had any regrets about being denied a transfer, he told Telefoot : "Maybe. I was a little disappointed. Once it's over, it's over, so do not think about it.
"I will keep working hard so these clubs eventually come back in the next transfer window. I am open to all offers. I am a football player, I like football. I do not close any door."
Lemar has made 29 appearances in all competitions in 2017-18, scoring three goals.