Shelvey has dropped out of favour in recent games with Curtis preferring to start Jack Cork, Leon Britton and Ki Sung-yueng in midfield instead.
"There has been a lot of speculation about Jonjo," Curtis told British media.
"He is out of the side at the moment and he is an England international, so I guess people are putting two and two together that if he is not in the team he will move in January.
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"But I have spoken to Jonjo and he wants to play his part. Unless things change, I expect him to be here."
The England international, who had not started a game for more than a month, was recalled to Swansea's starting line-up in the goalless draw against Crystal Palace on Monday, but was taken off barely 10 minutes into the second half.
"He is out of the team because of the form of others. He played on Monday and was a little bit disappointing," Curtis added.
"I feel it is a matter of time with Jonjo, potentially he is a great player and the class will always come through at the end."
Gomis, who has found the back of the net just once since August, has also been linked with other clubs in British media.
Curtis said he was unaware of any approaches and hopeful of retaining the Frenchman as well.
"I hope he will stay," Curtis said.
"As far as I am aware, there have been no enquiries about Bafe (Gomis). You see the speculation in the papers but the chairman certainly has not mentioned players going to me."
Swansea begin the new year with a trip to Old Trafford on Saturday, hoping to do the double on Manchester United after beating them at home in August.
(Reporting by Nayan Das in Bengaluru; editing by Amlan Chakraborty)
