Roberto Martinez wants captain Garry Monk to sign a long-term contract.
The 29-year-old has already seen his deal extended by a year after a clause in his contract was triggered.
But Martinez is in talks with him about signing on until 2011.
"The way this football club works now is that these things go down to performance," Martinez said.
"And when you get a performance like Garry Monk has put in over the last 10 months, it should be rewarded.
"We are trying to get him to sign a new long-term contract as a reward for the season he has had."
Martinez also revealed Stockport defender Ashley Williams is close to completing a permanent move to the Liberty Stadium.
The highly-rated 23-year-old joined initially on loan in March and made three appearances as the Swans secured the League One title.
Martinez is now hoping Williams can become his first signing of the close season.