The 23-year-old midfielder becomes a free agent next summer when his contract expires, and Leeds boss Simon Grayson is hoping he will stay.
Elland Road chief executive Shaun Harvey said of the club's attempts to tie up a deal: "Discussions have been ongoing since the August transfer window shut.
"We have made an offer to Jonny and we are waiting for a response."
Howson joined the Yorkshire club as a trainee when he was just nine years old back in 2007.
Source: Team Talk
Source: Team Talk