Strachan, who managed the Hoops between 2005 and 2009, was speaking on talkSPORT‘s Kick Off programme about Rodgers being in the frame to succeed Arsene Wenger at the Emirates after the Frenchman brought the curtain down on his 22-year stint in charge of the Gunners.
• READ MORE - Celtic boss Brendan Rodgers dismisses Arsenal link
With Arsenal searching for a replacement, Rodgers - who is on the cusp of leading Celtic to an historic double treble - is one of a handful of names along with former Borussia Dortmund coach Thomas Tuchel, ex-Barcelona head coach Luis Enrique and former Rangers and Everton midfielder Mikel Arteta.
Celtic’s majority shareholder Dermot Desmond took the unusual step of speaking publicly about the speculation, conceding that he wouldn’t stand in the Northern Irishman’s way if he was approached by Arsenal.
And Strachan reckons Rodgers’ experience managing Liverpool, as well as his time at Celtic, will stand him in good stead if Arsenal do come calling.
Strachan said: “As Celtic manager, you play in the Champions League and you have to deal with the top, top teams - so there’s preparation there. But also, Brendan has done it at Liverpool.
“Some of the managers who are being talked about [for the Arsenal job] have never been anywhere near winning the Premier League - like Brendan was at Liverpool.
“Celtic understood when they took him on that, if he did a great job - which he has done - he would get the call somewhere else.”
Having been in charge at Celtic himself, Strachan is only too aware of the pressures Rodgers will be facing, but believes it just strengthens Rodgers’ credentials.
Strachan added: “If he can do it at Celtic, he can do it anywhere. There’s a gap [between Arsenal’s level and Celtic’s level] but there’s no gap in terms of the stress you get as Celtic manager.
“When you’re at Celtic - if you can deal with the stress and the media, you can deal with it anywhere.”