Lealiifano joined from Brumbies on a short-term deal in August and is due to head back to the Super Rugby side in early 2018.
The fly-half, who was diagnosed with leukaemia last year but returned to the sport in July after revealing he was in remission, is yet to fully consider remaining at the Irish province longer than initially planned, but suggested he would be open to it.
"I can't look too far ahead. I'll go until the end of January and do the best I can," Lealiifano told BBC Sport.
"I think the most important thing is to help this team perform and help the other young guys that are in the Ulster set-up, to be able to groom them to be able to step up, that's sort of been my main goal. If something happens down the track, you definitely can't rule that out.
"I don't know how realistic [staying is], I haven't really explored it at the moment. Obviously, a lot of the fans and people have been in my ear to try and get me to stay. I'm really enjoying it so far and we've just got to stay with each week."
Photo by Getty Images. Caption: Christian Lealiifano is on loan at Ulster from Brumbies