Rangers are on the lookout for a new permanent following the departure of Pedro Caixinha in October.
Graeme Murty is in charge of the Gers’ first team at the moment and is doing a good job.
“Tommy would be perfect for Northern Ireland if Michael moved on,” Rodgers told The Scottish Sun. “He’d be absolutely brilliant.
“Tommy is one who has earned his stripes at St Johnstone in terms of the work he has done there to make them competitive. I think he would be perfect for the Northern Ireland job.
“For me, like the Rangers job, Derek McInnes and him would be stand-outs for that one. I really hope Tommy gets the chance, given the work he has done, to do it on a bigger stage, wherever it is.”
McInnes has been in charge of Aberdeen since 2013 and has done a wonderful job at the Pittodrie Stadium.
Wright has also been the manager of St Johnstone since 2013 and has made the Saints a very competitive team.
According to odds on Sky Bet, McInnes is the favourite for the Rangers managerial job with 4/6.
The chances of Wright getting the Ibrox job are rated at 28/1 on Sky Bet.