West Ham star Rice – who is of dual nationality – made his England debut in their 5-1 Euro 2020 qualifying win over Montenegro on Monday, having switched to Gareth Southgate's side despite appearing in three international friendlies for Ireland.
McClean, who played the full 90 minutes in Ireland's 1-0 victory against Georgia in Group D action on Tuesday, found himself in a similar position when it came to picking his international allegiances, but has insisted that his country are better off without players who are aiming to use them as a stepping stone.
"[Rice] said he was a proud Irishman. Then he said he was a proud Englishman. If he's both... good luck to him but I don't buy it," McClean told RTE Sport before the game.
"I think you're either one or the other. I was with Derry City when I got the call-up to play for the North and I turned it down because it's not my country, it's never been my country. I'm an Irishman.
Loved my first week away with @England . Special way to top it off getting my full competitive debut tonight in such a great performance from all the lads. Already looking forward to the summer pic.twitter.com/ysSJuvNB6a— Declan Rice (@_DeclanRice) March 25, 2019
"It's not just Declan, it's anyone else. If you're not proud to be here and we're a stepping stone then sod off and play for someone else.
"I'm an Irishman. I grew up on the island of Ireland, simple as that. We only want players here who want to play for Ireland, who feel Irish and are proud to be Irish."
Rice will return to club duty this week with West Ham, with a crucial home game in the Premier League against Everton to take in on Saturday.
Mclean, meanwhile, will be back in Championship action with Stoke this weekend, as they host Sheffield Wednesday.