The United captain, who just one year remaining on his current deal, is mulling over an offer that will make him the highest paid player at Elland Road.
Warnock is hoping Snodgrass accepts the offer as the United chief sees the Scot as a key part of his rebuilding job, which will get under way today when Portsmouth defender Jason Pearce becomes the club’s first signing of the summer in a £500,000 deal.
But if the in-demand winger opts to turn down the new contract offer then the Leeds chief still wants him to remain and lead the promotion push.
He said: “I would love to keep the likes of Snodgrass, irrespective of if he signs. I would like to keep him until Christmas. The chairman is in agreement with that, though of course you can never say never.
“Clubs in the Premier League would be interested in a player like Snodgrass and they might be able to agree a fee, I just don’t know. But I want Snod to stay.”
Snodgrass is not the only United player Warnock wants to tie down with Ross McCormack and Aidy White having also been offered new terms.
McCormack, like fellow countryman Snodgrass, has a year left on his existing deal, while White is out of contract in a few weeks.
Warnock added: “Leeds is a unique situation in that we can’t say, hand on heart, that one of those players will re-sign. Yet, they might all re-sign.
“I have spoken to Snod and not really given a deadline as such. But I don’t think we can go too far beyond the end of May, really. By the time I come back off holiday, we will need to know where I am batting so we can progress.
“Even if we don’t like to accept we might lose players, by that time if they haven’t re-signed then we have to look seriously at what we do.”
One player expected to be at Elland Road next year is Pearce, who according to sources on the south coast agreed a three-year deal with Leeds several weeks ago.
The 24-year-old enjoyed an impressive season for relegated Pompey, a point underlined by him scooping seven of the nine Player of the Year awards at Fratton Park.
Warnock, while refusing to confirm the identity of the player who will sign today, said: “I am looking forward to getting my first signing in and then moving on to the next.”