Warnock never worked for the Leeds United owner, but spent a year at Elland Road prior to his arrival.
Warnock believes Monk is a sensible appointment
Monk became the seventh boss of Cellino's reign as Leeds owner last week, having agreed a one-year rolling contract at Elland Road.
The Italian has big ambitions for the coming campaign, even offering refunds of up to 50 per cent to season ticket holders if the club fails to make the top six.
Cellino has offered Leeds fans a big incentive
And Warnock, who managed Leeds from 2012 to 2013, believes the Yorkshire side can bridge the gap next season - if Cellino leaves Monk to his own devices.
The 67-year-old told Radio Yorkshire: "Garry Monk’s a sensible appointment and I think if he (Cellino) lets him manage, helps him and supports him by letting him bring the players in that he knows and not just anybody - then you never know.
"It’s not going to take much (to make Leeds contenders). I think the Championship’s wide open."
Monk arrives at Leeds with Premier League and European experience
Monk, who led Swansea City to their highest-ever Premier League finish in 2014-15, has been out of work since leaving the Liberty Stadium last December.
And Warnock added: "He’s obviously thought there’s not a lot else around for him at the moment so why not see what he can do.
"They’ve got some very, very young players now - the nucleus of a decent side."
With a squad of more than 20 players to work with, Monk is unlikely to make wholesale changes to his Whites squad this summer.
So far, only Scott Wootton and Mirco Antenucci have been allowed to leave Elland Road, though all three loan players have returned to their parent clubs.
Antenucci was released by Leeds, along with Wootton