Steve McClaren's job as Newcastle boss is also under serious scrutiny, with many supporters feeling it's time for a change after their latest away defeat.
But the former England manager appears to have the backing of Mike Ashley and Co, something which Lee believes will see him stay at the club; plus the lack of eligible top class coaches available to the St James' Park hierarchy.
'I don't know who they would replace him with, who is Mike Ashley actually going to go out and get? Not anybody huge because they cost a lot of money,' admitted the ex-England international.
'They gave him [McClaren] £80million and he's got a place on the board and as I say, is Mike Ashley going to go out and get a big name? A David Moyes? And would they work under him?
'With the restraints he puts on the manager, I would not have thought so. I don't know who you would replace him with and it depends on how much say he'd have because that's what is always in the dark at Newcastle.'
Providing the Magpies avoid relegation to the Championship, many would expect the club to continue their big spending in the summer transfer window, once the TV money comes to fruition.
But Lee believes his old side missed a trick already by letting new Southampton signing Charlie Austin slip through their grasp for a bargain £4m.
The former Queens Park Rangers star netted the winning goal on his debut against Manchester United and looks to be money well spent by Ronald Koeman.
He said: 'It's a million dollar question, it's why McClaren gets paid a lot of money but Charlie Austin was it for me and he went to Southampton for £4m.
'He was the one, he would have suited Newcastle as he's proven he can score in the Premier League and look at Bournemouth who took a chance on Benik Afobe, who has started very well.'
McClaren's men looked to be heading the right direction when Aleksandar Mitrovic scored the only goal to beat West Bromwich Albion and move them out of the bottom three.
But the abysmal display at Chelsea has fans worried once again about their Premier League survival, with a lack of fight evident during the mauling in West London.
Despite this, the 50-year-old feels the Magpies have just about enough to escape but worries about the club's lack of goals.
'I do genuinely think we'll be OK. I watched Aston Villa, it could be worse; they were awful,' he added.
'Norwich are on the slide, I feel Swansea are worse than us and Bournemouth will be down there but I love the way they play football and Sunderland are always going to be down there but they have a goalscorer.
'You look at teams down there and Sunderland have a natural goalscorer in Jermain Defoe and that's something Newcastle haven't got. That needs to be addressed.'