Evans brought Bridcutt to Elland Road on loan from Sunderland last season, and he impressed at the Yorkshire club.
Bridcutt was immediately made one of Leeds top targets this summer, but progress has been slow in the transfer.
Sunderland and Leeds have had difficultly negotiating a price, but the Yorkshire Evening Post suggest that Bridcutt is now finally edging towards moving back to the Whites.
Evans feels that Bridcutt’s arrival at Leeds will help strengthen their side considerably, and he believes that Monk will need to continue to spend if he is to get the Whites into the top six.
“Every day that goes past they have more of a chance of getting into the play offs,” Evans said, when asked whether Leeds could get promoted this season.
“Cook was always going to be sold, but Liam Bridcutt is a must signing for them!
“If Garry can get one or two more players, they can get in the top six.”
When Evans was in charge, he promised that he would guide Leeds into the play offs in the upcoming season, but his statements were not enough to convince Massimo Cellino to keep him at the helm.
Monk has made seven new signings at Leeds so far this summer, with Bridcutt widely expected to be his eighth addition.
Leeds are set to play Queens Park Rangers on the first day of the new season at the weekend.