Belfast-born Kearns, who last season had a loan spell with the Spireites' local rivals Rotherham, is expected to complete his temporary move to the League Two leaders on Tuesday.
The 22-year-old has been brought in by manager Paul Cook following the injury to Dan Gardner, with Gary Roberts also thought to be nursing a slight problem.
Gardner is facing a spell on the sidelines with an ankle injury following a challenge involving Accrington midfielder Peter Murphy on Saturday. He will see a specialist on Tuesday to determine the extent of the problem, although initial scans have revealed no bone fracture.
Kearns began his career in the youth ranks at West Ham but was released in 2010 and signed for League of Ireland side Dundalk, which is where he first came to the attention of Cook who was in charge of Sligo Rovers at the same time.
He joined Peterborough in the summer of 2011 and made more than 20 appearances for Posh, then in the Championship, during his first season at London Road.
The following campaign was spent on loan at York and Rotherham and he played against Chesterfield in the Millers' 1-0 win at the New York Stadium in February of last year.
Kearns has made 15 appearances for Peterborough this season. The last of those came on February 5 in a 2-2 home draw with Swindon in the first leg of the Johnstone's Paint Trophy Southern Area final.
His involvement in that game rules out any possibility of him playing against his parent club at Wembley when the Spireites face Posh in the Johnstone's Paint Trophy final on March 30.