Independent.ie understands that Rice is on the shortlist for the vacant role, with the League Two club formally approaching the FAI in order to open discussions with their employee.
The 38-year-old is in the running to replace Scott Lindsay as boss of the League Two promotion chasers.
Dubliner Gavin Gunning is currently operating in a caretaker capacity with Swindon after Lindsay departed for Crawley Town.
However, Rice is very much in the frame for the permanent gig, a development that would create another staff headache for Stephen Kenny with a view to the forthcoming European Championship campaign.
Rice assumed the role left vacant by the departure of Ruaidhri Higgins for Derry City in the spring of 2021 but was given extra responsibility in the latter half of last year after John Eustace’s short-lived stay as a coach filling the shoes of Anthony Barry.
Kenny will be replacing Eustace before the Euros tilt starts in March, but it would be a blow to lose Rice and be forced to find another new member of staff.
For Rice, it would represent a significant breakthrough, given that he never made a senior appearance in England as a player.
He spent time with Coventry as a trainee but came home to make his name in the League of Ireland with Bohemians before enjoying an extremely successful spell with Shamrock Rovers.
Rice always had an eye on the coaching sphere and was involved in the development of the likes of Nathan Collins and Jason Knight during his work with Dublin and District Schoolboy League (DDSL) development sides before working with the Rovers underage set-up.
The reputation he developed allowed him to get a second chance across the water as a professional development coach with the Crystal Palace U-23 side, where he made a strong impression.
He was tempted away from that role in the summer of 2021 to link up with his former manager Kenny as a full-time FAI staff member after a brief period of double jobbing.
Last year, Rice was floated as a potential candidate to be Shamrock Rovers boss when it appeared that Stephen Bradley was on his way to Lincoln City.
But now, it’s Rice who could end up embarking on a new start in the English lower leagues by joining a club sitting sixth in the fourth tier, which has made headlines on and off the pitch in recent years.
Australian Clem Morfuni took sole ownership in 2021 after former Irish underage international Lee Power’s eventful period at the helm, which overlapped with his time with Waterford.