Neilson has been granted responsibility for dealing with targets, although Levein has acted as a mentor during these proceedings.
Hearts have been linked with moves for out-of-contract St Mirren defender Darren McGregor and Morgaro Gomis, the midfielder released by Dundee United, since the end of the season. Whoever agrees to join Hearts this summer, Neilson has admitted that he will be indebted to Levein.
"I don't think I'd be able to do it without him beside me, just to help and instruct me on what to do here and there, and how to structure things," said the coach. "Craig has been fantastic with me, giving me advice and helping me through it. If I need to bounce anything off him then he's there."
Kilmarnock last night confirmed Sandy Clark has left his role as assistant manager.