United sacked manager Jose Mourinho on Tuesday after having suffered their worst start to a season for 28 years.
Although United would neither confirm nor deny media reports about who would take charge, Norwegian Solskjaer and Phelan are "clear front runners" and a decision would be made shortly.
It is believed Phelan will be Solkjaer's assistant at United until the end of the Premier League season.
55-year-old Phelan was Sir Alex Ferguson's right-hand man at United from 2008-2013, playing his part in three Premier League title victories, a UEFA Champions League triumph, two League Cup wins and a FIFA Club World Cup.
The announcement of Phelan's appointment as Mariners sporting director in July was considered a major coup for the A-League club.
The former Red Devils player and coach was tasked with rejuvenating the struggling Central Coast side's youth development programs.
Phelan was not required to move to Australia full-time for the role, instead traveling from his Manchester home to Gosford a few times a year to run coaching clinics and help oversee the ongoing coaching philosophy of the A-League outfit.
It is not clear if he will need to step down from his role with the Mariners if a short-term coaching return to Old Trafford comes to fruition.
