The centre-back is set to leave Rangers at the end of the season with his contract due to expire and the prospect of signing an extension not forthcoming.
According to the Scottish Sun, Nottingham Forest and West Brom are keen to land the 29-year-old who has been a key figure at Ibrox since arriving in 2018.
Across the past four seasons Goldson has played 195 times. He has missed or not been chosen for just ten matches during that time. Remarkable consistency for a player who made just 16 appearances in his final two years at Brighton & Hove Albion before the switch to Govan.
He missed ten months of action in 2017 due to preventative surgery following the discovery of a heart defect.
Now Forest and West Brom are battling it out to bring Goldson back to English football with both eyeing promotion to the Premier League.
The Baggies sit fifth with Forest five points behind in eighth.
Rangers are unlikely to want to lose the player this month with the club top of the Premiership by four points with a title win all but securing Champions League football.
Giovanni van Bronckhorst has already tied down John Souttar on a pre-contract agreement, with the Scotland international a potential Goldson replacement.
The Premiership league leaders are keen to bring the player to Ibrox this month but have already had a bid of £300,000 rejected by Hearts.
It is understood the Tynecastle Park club value the player at upwards of £500,000.
Robbie Neilson revealed the player could be involved against Celtic on Wednesday after being left out of the squad which beat Auchinleck Talbot 5-0 due to an Achilles injury.
"We’ve had a bid in, which has been knocked out the ballpark, so we will wait and see if anything else comes in," he said.
“He will be in the squad for Wednesday until something changes.
"We value John very highly and if anyone is going to take him in this window, they’ll need to pay for him because we are aiming for the Scottish Cup and European football and we need to keep our best players.”