Rodgers guided Swansea to promotion to the Premier League in his first season in charge of the club.
Swansea have also made an impressive start to their spell in the Premier League.
Jenkins told the South Wales Evening Post: “We will be sitting down with Brendan to look at sorting out a longer-term deal over the next few months.
“Brendan’s services are already secured as he is on a one-year rolling contract, but naturally we want to secure him in the long term.
“Brendan and I speak at least three times a week, maybe every day, and we have already talked through his thoughts and mine on extending his contract.
“Brendan likes working here. He is happy and he is settled, and we will look to get something sorted out.”
