Venture capitalists are keen to draw on his furniture sector expertise at one of MFI's biggest rivals and are understood to have sounded Favell out.
Favell joined Wyevale last August to lead a turnaround, but the store group is now being sold to tycoon Sir Tom Hunter.
Before joining Wyevale, Favell spent six years at 220-store Magnet, which was sold in 2001 to manufacturing and retail giant Nobia.
A shortlist of bidders for MFI is understood to be near completion after the auction process began on Monday, the closing date for first round bids.
Sources close to the bidding process, which is being overseen by investment bank Dresdner Kleinwort Wasserstein, said that MFI hopes to conclude the disposal of its retail operations by the end of next month.
Alchemy, Apax, Argyll Partners and Merchant Equity are among the private equity firms interested in MFI which, despite its difficulties, still accounts for about a third of the UK's kitchen sales.
A trade sale of MFI is thought to be unlikely, but Carpetright, DFS, Dreams and Land of Leather are all interested in cherry-picking from MFI's portfolio of stores.
MFI is likely to pay about£200 million to a bidder in order to rid itself of the problem retail division. The disposal is complicated by a£150 million pension deficit and product supply arrangements.
Retail Knowledge Bank senior partner Robert Clark understood why MFI might appeal to private equity buyers. He said: 'MFI has defied gravity before. There is an undoubted opportunity, given its sales of about£800 million.'
However, he warned: 'It needs to restore momentum very quickly, because brands can atrophy very quickly.'
He believes the way in which the link between retail and manufacturing is dealt with will be crucial both for MFI Retail's buyer and the rump business.
MFI, led by Matthew Ingle, will focus on its profitable Howden joinery arm after unloading the stores business, which lost£85 million last year.
Both Favell and MFI were unavailable for comment.