The 600-strong workforce were told this week by bank bosses that they will be closing the building and relocating to another site in the area.
It comes 30 years after the purpose built centre opened on the prime waterfront site in the town with almost 1,000 people working there at its height.
But RBS – owned by the NatWest Group – has told the Tele it is fully committed to the area with no plans to leave Inverclyde – with negotiations for a new premises at an advanced stage.
A NatWest Group spokesperson said: “The Royal Bank of Scotland is proud to be a major employer in Greenock and remains committed to the local area.
“Having recently celebrated 30 years at Cartsdyke Avenue, it is right that we are now looking to secure a more modern office space.
“This will also be in the local Greenock area and we intend to announce these plans in the near future.”
The RBS Mortgage Centre opened in 1995 and was regarded as a flagship centre for the global banking firm, starting with 50 members of staff and increasing to its height in the early 2000s.
Two years ago concerns were raised by SNP MP Ronnie Cowan about the decision to axe 30 jobs at the centre, at a time when there were a number of job losses in the area.
In recent years Inverclyde has suffered a number of blows with EE closing its call centre in Greenock and moving out of the area, as well as Amazon and IBM closing.
But RBS has repeatedly reassured local leaders that it is are fully committed to Inverclyde and its local workforce.
A source told the Tele: “Staff were told about the decision to move. But the building is ageing and is need of repair so it was not surprise.
“It has not been confirmed yet where we will move to in Greenock.
“Since the pandemic people work at home most of the time and come in maybe one day a week. The building is pretty empty at times.”