The 18-year-old midfielder has 12 months remaining on his contract and is expected to decide on his future in the summer, having drawn interest from Borussia Dortmund and other clubs.
Talks over a new deal at Villa had previously stalled but Gerrard has made clear his desire for the England under-19 international to stay.
“Hopefully he is going to be a big player for Aston Villa,” he said. “We want him to stay here long-term. We believe this is the best place for Carney. I hope that situation progresses in a positive way.”
Chukwuemeka made his 11th Premier League appearance of the season coming off the bench in Tuesday’s 2-1 defeat to Premier League title challengers Liverpool.
It was the second match in succession he had been the first substitute introduced by Gerrard, who said: “I think again me and my staff have shown huge trust putting an 18-year-old in but we wouldn’t do it if we didn’t think he was ready or had the ability to cope.
“It will be a good experience and a learning one for him being on the pitch around so much quality.
“In training he has been fantastic. I’ve said many times if these kids deserve to go on the pitch ahead of those who are older, I’ll put them on.”