It’s understood Mellon, 48, is the man United sporting director Tony Asghar hopes to appoint to the Tannadice hot seat.
The Paisley-born coach – under contract at Tranmere until next summer – has made it clear he wants the chance to manage in Scotland’s top flight.
Mellon has an impressive record in the lower leagues down south, also bossing Fleetwood Town, Barnsley (as caretaker) and Shrewsbury Town.
Rovers were relegated from League One last month after a vote to call the bottom two divisions early on a points-per-game basis.
Former England manager Steve McClaren this week rejected the opportunity to take over from Neilson, while Asghar has also spoken to SFA performance director Malky Mackay and ex-United captain Jon Daly about the job.
St Johnstone legend Tommy Wright and former Tannadice ace Billy McKinlay have also been linked with the post.
