The Scot is favourite to take over at the Stadium of Light and could bring with him the following players from Everton, Manchester United and Real Sociedad.
Allardyce will depart the Stadium of Light having failed to add to the squad he kept afloat with a game to spare, leaving Moyes (or other) to oversee the Mackems' summer recruitment drive.
With less than a month until the new season begins, the Scot may need to act fast, which could see him turn to those with whom he's already familiar.
According to the Sunderland Echo, Allardyce wanted a new right-back, striker and number 10, in addition to last season's loan star Yann M'Vila.
Here are four of Moyes' old charges who could fill those gaps...
Right-back - Rafael da Silva
Moyes inherited Rafael at Manchester United, using him 19 times in the Premier League - his highest seasonal tally in English league campaign bar the previous one. However, the Brazilian's Old Trafford career nosedived under Louis van Gaal, leading to his exit for Lyon a year ago. Les Gones qualified for the Champions League next term, but Rafael could yet be coaxed away.
Central midfield - Darron Gibson
Gibson's Everton career looked to be coming to an end this summer, but the Irishman, signed by Moyes in 2012, has since renewed his contract at Goodison Park. However, with James McCarthy, Tom Cleverley, Mo Besic and Gareth Barry to contend with, regular football seems unlikely this season - especially if the Toffees add another player in his position, as expected. A move to Sunderland could appeal.
Number 10 - Adnan Januzaj
The Belgian was heralded a future superstar after being blooded by Moyes in late 2013, however, he failed to kick on under Van Gaal and spent almost the entirety of last season struggling to get games at both United and Borussia Dortmund. A reunion on Wearside would be ideal for both parties.
Striker - Jonathas de Jesus
Moyes paid a reported £6 million to bring Jonathas to Real Sociedad a year ago, however, the Brazilian never showed his true colours under to Scot. He went on to score all but one of his seven goals last season after Moyes was sacked, but perhaps they could get it right at the second time of asking. At 6ft 3, Jonathas, who scored 14 La Liga goals the season before last, is the quintessential Jermain Defoe partner.