Manchester United manager Louis van Gaal has refused to rule out the possibility of signing goalkeeper Victor Valdes.
Manchester City boss Manuel Pellegrini says he is confident that England goalkeeper Joe Hart will sign a new contract.
Sky Bet have priced up when Poyet's first Premier League win will come and offer 5/1 that it does at the Liberty Stadium on October 19.
They make it more likely that the Uruguayan's first three-point haul comes when the Black Cats play host to North East rivals Newcastle eight days later.
That is priced at 15/8 with 11/2 chalked up about the first win coming at Hull in their following match.
Poyet has signed a two-year deal but is just 7/4 to leave his post by the end of the current season. He is 2/5 to still be in charge for the club's final game of the season.
The former Brighton boss has been appointed as head coach following the club's poor start to the season and Paolo Di Canio's subsequent dismissal.
Sunderland are currently bottom of the Premier League with just a single point collected from their first seven matches.
For the more optimistic fan, Poyet is 16/1 to lead the club to a trophy this season - they are still in the League Cup and have the FA Cup to come in the New Year - while it's 7/2 that the new boss wins a manager of the month award in the current campaign.