David Moyes revealed on Monday that the two clubs have been in contact regarding the midfielder, with an initial £25.9 million offer rejected, and an improved package had been submitted - thought to be worth £30m plus add-ons.
"I do not think that Cesc will leave Barca," Puyol stated on the club's official Twitter feed.
| TRANSFER TALK
|1/1||Cesc Fabregas is 1/1 with BetVictor to join Manchester United
Puyol admits the news of his departure came as a surprise but has vowed to turn in impressive performances next season as the best way of showing support to the Spaniard.
"What has happened with Tito is a huge blow for us. We did not see this coming and the team suffers a lot," Puyol told reporters.
"Tito has already shown us that he is really strong and he is ready to battle. The team will be by his side any time he needs us.
"He has asked us to give our all on the pitch. That would be the best way to support him and we will do do our utmost to give him some joy."
The veteran defender also backed new signing Neymar to impress next season, with former AC Milan boss Arrigo Sacchi suggesting he could fail.
He added: "Neymar is a superb player. He is still young, yet already has a lot of experience. He is ready to play for Barcelona."