The Line of Duty star is a self-confessed Celtic fanatic but has family ties to Rangers through his wife, Tianna Chanel Flynn, whose dad is a San Francisco 49ers fan.
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The 49ers are set to be involved in a takeover of Rangers by a US consortium.
A deal has been agreed in principle with the American consortium after talks between Paraag Marathe of 49ers Enterprises and health insurance tycoon Andrew Cavenagh and the Ibrox club progressed.
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Compston said he will not be discussing what the new owners could bring to Rangers, wanting to focus on his own club, The Scottish Sun reports.
He appeared on talkSPORT this morning, March 5, joining fellow Celtic fan Alan Brazil and former Aston Villa star Gabby Agbonlahor on the Sports Breakfast show.
He said: “Ach I’m on the other side of the city, let them deal with that.
“My father-in-law is a 49ers fan so I’ve told him if that goes through, he’s banned from the house.
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“It’s a great time to be a Celtic fan.
“I was born in ’84 so grew up in the 90s and it was dark times for us.
“People always ask me if I get bored of winning. Not at all.
“Long may it continue.”
Celtic are currently on course for another treble, with Rangers 16 points behind in the Premiership.
Brendan Rodgers also looks set to stay at the club.