The 38-year-old was appointed as Leeds boss earlier this summer after Steve Evans - who only replaced Uwe Rosler in October - was not given a contract extension for 2016-17.
The former Swansea City player and manager is the seventh managerial appointment since Cellino took control of the club a little over two years ago, which illustrates just how ruthless the Italian businessman can be regarding his head coaches.
Time is unlikely to be a luxury afforded to Monk, but McPhail, who spent nine years at Elland Road until 2004, is desperate to see him given time to inspire United's return to the Premier League after a 12-year absence.
The 36-year-old told LUTV: "I'm not too familiar with the ins and outs of the board and the chairman, but I just hope the manager gets a bit of time to produce what he wants.
"He's a good young manager. I played against Garry for Cardiff and he seems a really decent bloke. I think he'll bring fresh ideas and I just hope he'll be given time to do what he has to do."
Monk's only previous job in management came at Swansea, where he survived a little under two years before getting the sack last December - good innings considering that it was his first job and it came at an established Premier League club.