The Sun says Barca president Joan Laporta has held talks with Massimo Moratti over a move.
Barcelona are keen on keeping the Cameroon international at the club, but Eto’o has only one year left on his contract.
Laporta said: “There was a meeting with Moratti, because Mourinho likes Eto’o a lot.
“We want him to renew his contract but not at any cost.”