Former Watford and Reading manager Rodgers, who guided the club to promotion in his first season in charge, joined on a one-year rolling contract in the summer of 2010 and is still operating under those terms.
But with the highly-rated Northern Irishman having helped the Swans make a competitive start to their maiden Premier League campaign, 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."
He added: "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."
Source: PA
Source: PA