The 25-year-old impressed for Chile at the World Cup until they were eliminated by hosts Brazil in the last 16, following a season in which he scored 19 goals in 34 league appearances for Barca.
But despite his form, there has been persistent speculation that Alexis could depart Camp Nou, with reported interest from Serie A champions Juventus and Premier League club Arsenal.
"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."
The Chilean has also been mentioned as part of a possible deal that could take Liverpool striker Luis Suarez to Spain.