The 'Price Tag' singer was recently reported to have snubbed Cohen backstage on the show after he tried to congratulate for her the programme's success.
However, it is now claimed that Cohen has had a "frank discussion" with Jessie J to praise her for her work on the show, and has asked her back for its second series.
"It was a positive and frank discussion that ended on very good terms," a senior source told The Mirror.
"There was clearly a misunderstanding before when they were supposed to meet.
"But that is now water under the bridge. He hasn't got a problem with Jessie and wants to keep working with her."
Jessie J previously angered producers after describing parts of the show as "lame" and admitting that she didn't watch the series after it was recorded.
The Voice UK continues next Saturday (May 19) at 6.30pm on BBC One, when Jessie J and Danny O'Donoghue's teams will battle it out to stay in the competition.