Lemar is a top target for the Gunners this summer.
Keeping Sanchez is also a top priority, with Arsene Wenger insisting the Chilean is going nowhere.
But according to Sun journalist Martin Lipton, Wenger will have to sacrifice Sanchez to get the Monaco man.
He told TalkSPORT: "Monaco have a key bargaining chip in Thomas Lemar, who they know Arsenal are desperate to land.
"My understanding is while they would like to take Sanchez and make this offer [of £45m], they are willing to use this bargaining chip to see if they can get him.
"They've got money to spend, they see Sanchez as the answer and they are willing to give him £300k a week. The thing is with Monaco, you don't have to pay tax either.
"I know Wenger doesn't want to lose Sanchez but if this comes an offer with Lemar as a part of the negotiations, it may be the best option."
Lipton added: "Wenger has been very firm in the last couple of weeks insisting he's not going to go, talking about the meeting he had with Sanchez and that he's going nowhere.
"He also said a week before Van Persie went that he was going nowhere, a week before Fabregas went that he was going nowhere, a week before Nasri went that he was going nowhere.
"There's a pattern there for Arsenal fans.
"While Sanchez wants to go to City, Wenger is reluctant to sell him to an English club which is absolutely understandable, unless you're Antonio Conte it seems.
"But he didn't say he wouldn't sell him to another club."
