Reports emerged last week that the Argentine turned down a lucrative new deal to extend his stay at the Catalans, further fueling speculation that he may move on when his contract expires in 2018.
However, Mestre insists there are no problems and that talks with the player regarding an extension are going smoothly.
"The truth is everything looks good," Mestre told TV3.
"Everything will end up well. If they're saying there are problems [with the talks] in Madrid, then I'm delighted to be able to contradict them.
"Lionel Messi's contract renewal is on track. I'd say we've hit the final straight and in a few weeks there will be news. I cannot give an exact date, but it won't be long."