The Croatia international was linked with a €90m move to PSG, though ultimately committed to Barca in the opening week of the season.
Mestre admits Barca had to fight off interested clubs for Rakitic before the summer market shut.
"I really like Ivan, he's a good person," he said. "A club that has a state behind them came to pick him up.
"We cannot fight this."
Rakitic also confirmed this week: "There were offers, big clubs wanted me but honestly, I talked to my wife and we concluded that I was happy here and proud to be part of this great club."