Fabregas joined Arsenal from Barcelona as a 16-year-old in 2003, but has been linked with a return to Spain in recent months.
Both Barcelona and Real Madrid are keen on the Spain international.
Agent Joseba Diaz told BBC Sport: “These stories are normal but there is absolutely no truth in them whatsoever.
“Cesc is happy for Thierry as they are friends. But he can’t wait to start the season, he is a key man for Arsenal.”
He added: “Thierry was a very important player for them and it is normal that now he is no longer there, everyone thinks it is very bad news for the club.
“But Arsenal are going to buy a lot of good players and they are going to be a major team both in the Premier League and Champions League.
“Without Thierry, Cesc is one of the best players at Arsenal and this is fine for him, he is happy with the responsibility.
“At the moment Cesc is on holiday, but he is very excited about the new campaign.”
