The Black Cats are expected to appoint Poyet in the next 24 hours, with the club sitting at the bottom of the Premier League table and the dressing room in need of a lift following Paolo Di Canio's brief, ill-fated spell in charge.
Sunderland have claimed to be taking their time over appointing Di Canio's replacement and considering all their options, but Mills believes that Poyet - who was the early favourite - may have been holding out for the Fulham position to become available before he was prepared to commit to the Black Cats.
Mills told Sky Sports News Radio: "There are managers who would prefer to stay in London. That is where Poyet was when he played at Chelsea and it is a little bit more cosmopolitan and easier to attract players to a club like Fulham than it is to the North East.
"That is not being derogatory to Sunderland at all. I think everyone understands that, foreign players especially, prefer to be in London. Plus, they (Sunderland) have had a couple of hard games so maybe he thought: 'Let's just wait and see.'
"Now there is less likelihood of the Fulham job becoming available, Poyet is probably thinking: 'It's either take this, or wait around for another six months, perhaps a year, for another decent job to come up.'"
Mills is not sure if Poyet is "a good fit" and says the former Brighton boss comes with "a bit of baggage".
Listen to the full interview with Sky Sports News Radio to see what Mills believes Poyet has to do at Sunderland to keep them in the Premier League.
Former Sunderland winger John Oster is "quite excited" by the impending appointment Poyet and believes the Uruguayan will get Sunderland playing attractive football if he is given time to stamp his identity on the side.