The Belgium international has been with the Club since 2008 and has made 348 appearances to date and is City’s most successful captain of all time.
Now, with his current deal set to expire this summer, the Blues’ boss has said the Club are in discussions with the 32-year-old to extend his City stay beyond 2019.
“Yes, we are considering it and we are talking about,” said Pep.
“I would like him to stay. He is our captain and has been here 10 years.
“We saw in the last games against Southampton and Liverpool that he is a huge personality.
“Obviously, the only problem has been his injuries.”
Pep also says he is lucky to have four top central defenders and that each have their individual strengths.
“One against one, absolutely we are better with Vincent,” he said.
The boss also says he will be doing all in his power to win every competition City are in this season.
The Blues are in second spot in the Premier League, semi-finalists in the Carabao Cup; in the last 32 of the FA Cup and last 16 of the Champions League.
“I prefer to try and do as well as we can, and I like to be in the four competitions for as long possible,” he said.
“In the cup competitions, we take it seriously. Versus Rotherham we played with nine players who didn’t play against Liverpool, but it was still a good selection.
“In many ways it’s perfect - 70 minutes for Kevin on Sunday, and he can try and play longer next time. That is great.
“It is essential to have a strong squad to compete on all fronts, because without quality you cannot win one, never mind four.
“Not just in England, in any league in the world. Every team has to be top with huge players.
“We need to respect our opponents. My analysts have prepared a report, and we want to be at Wembley.”