The 21-year-old's current deal is set to expire at the end of the season, but he has worked his way into Stuart Gray's first-team plans since returning from a successful loan spell at Plymouth.
Lavery scored his first Championship goals on his return to Hillsborough, netting twice in January's 6-0 demolition of Leeds, and he has been involved ever since.
The Northern Ireland under-21 international would be free to leave Wednesday in the summer, but he is hopeful of extending his stay in South Yorkshire.
"My representatives are speaking to Wednesday over getting it extended," Lavery told the Sheffield Star.
"I am leaving it to them. I am not getting involved at all. That's for them to work out.
"I would be happy to stay. The club have been good with me. They have helped me with my development.
"I've just got to keep doing what I am doing at the moment. I am putting in good performances.
"I just need to keep playing well and hopefully let my football do the talking and go from there."