Celtic are on the lookout for a new manager after Neil Lennon left the club last month and have been linked with several names.
The club are claimed to be in contact with former Bournemouth manager Eddie Howe, but Scotland boss Clarke is also believed to be in the running for the job.
McManus believes that the Scotland manager would not accept the job now as he will be looking to impress in the European Championship.
But he feels the 57-year-old will accept an offer from Celtic in the summer and believes his experience in Scotland makes him a great fit at Hampden Park.
The former striker stressed that the Celtic fans would accept Clarke as their new manager given his record.
McManus said on PLZ Soccer: “I think if Steve Clarke gets offered the Celtic job, he would take it.
“I don’t think he is going to take it now.
“I think he has got a real job to do in the Euros, but if Scotland can do well in the Euros, his stock will be up.
“I think Celtic could do worse than go for Steve Clarke, to be honest.
“He ticks a lot of boxes in terms of Scottish football.
“He is experienced here, and I don’t think Celtic fans would be too disappointed if it was him.”
Celtic are assessing their options and it remains to be seen who their first choice is.