Poyet saw his Sunderland side pick up seven points from their four matches in January, including a 4-1 win over relegation rivals Fulham at Craven Cottage.
The Black Cats also defeated Stoke 1-0 at home and drew 2-2 with Southampton as well as reaching the Capital One Cup final with a two-legged semi-final success against Manchester United.
Crystal Palace had a similar league record under Pulis with 1-0 home victories over Stoke and Hull along with a 1-1 draw with Norwich, while their only defeat came at Tottenham.
Mourinho's Chelsea side were unbeaten during January with away wins at Southampton and Hull and a 3-1 victory over Manchester United at Stamford Bridge, where they also drew 0-0 with West Ham.
Manchester City were unstoppable under Pellegrini during January with four wins from their four games as Swansea, Newcastle and Tottenham were all beaten on the road, while Cardiff went down 4-2 at the Etihad.
City midfielder Yaya Toure is one of the four nominees for the Player of the Month award for January after playing a key role in those four victories with goals against Swansea, Cardiff and Spurs.
Adam Johnson, Santi Cazorla and Luis Suarez are also in contention for the monthly gong.
England winger Johnson hit a purple patch for Sunderland during January with five goals, including a hat-trick at Fulham and the winner against Stoke.
Cazorla played a key role in the Arsenal midfield by netting three Premier League goals during the month, including a double in the 2-0 home win over Fulham.
Striker Suarez, the Premier League's leading goalscorer, was on target four times as Liverpool claimed 10 points from their four matches in January.
Both Suarez and Pellegrini are in contention for back-to-back awards after picking up the prizes for December.