The 25-year-old impressed for Chile at the FIFA World Cup until they were eliminated by hosts Brazil in the last 16.
Alexis' form at the marquee tournament was a continuation of a fine domestic season in which he scored 19 goals in 34 league appearances for Barca.
Despite that return, there has been persistent speculation that Alexis could depart Camp Nou, with Italian champions Juventus reportedly interested, while there have been suggestions he could be used as a makeweight in a deal for Liverpool's Luis Suarez.
Bartomeu has now revealed that bids have been lodged for Alexis, but the club want to retain his services.
"I can confirm we have received offers from several clubs for Alexis Sanchez," he said at a press conference. "Not just for what he has done at the World Cup but for what he has done before.
"He's a player there in the market that people have got an eye on but he's our player for the moment and he's a basic member of the way our team plays.
"He fits our system, he had a magnificent season last season. He scored a lot of goals, provided assists, had a lot of the ball.
"He's a player we would like to have with us next season. But we are getting a lot of calls from clubs who are making offers to buy Alexis Sanchez."
