However, the singer said he would support Scotland leaving the union "if it was good" for the country.
Speaking to BBC Scotland's The Nine programme, Sir Rod also said he believes Boris Johnson "will sort it out", when asked about Brexit.
He said: "I'm somewhat of a traditionalist. It would be a shame to see the British isles break up, it would be a shame to see that blue off the Union Jack.
"But if it's good for Scotland then I'm happy."
Sir Rod previously spoke out against the idea of Scottish independence ahead of the 2014 referendum, alongside a number of British celebrities.
When asked about the current political climate, he said: "We're in a muddle, but I think Boris will sort it out.
"We have to be patient.
"What I do know is that I was always a remainer. I didn't see why we had to leave. Maybe it's something that I'm missing, I don't know, but I'm still a remainer.
"I know Boris is going to get us out."
Sir Rod, who described Scotland as his "spiritual home", said the upcoming General Election is of the "utmost importance".
He added: "It's a once in a lifetime, this election.
"I don't know what the outcome is going to be, I really don't."