The move would create state-of-the-art new facilities for students, and help breath new life into the struggling town centre, which has been hit by successive store closures in recent years.
It has the support of the North East LEP, the North East Chamber of Commerce and various local businesses.
But a bid to the Levelling Up Fund to pay for the project seems to have been unsuccessful, with no cash emerging after the Budget.
However, champions of the project say there are other irons in the fire, and it is hoped funding will come through from other pots.
Cllr Tracey Dixon, leader of South Tyneside Council, said: “We are naturally disappointed that we were unsuccessful in our Levelling Up Fund bid.
“However, we are undeterred in our ambition to relocate the college into the heart of South Shields town centre and we will continue to lobby government for alternative sources of funding.
“In fact, the college has already been successful with an Expression of Interest to the Department for Education’s (DfE) Capital Transformation Fund bidding process and have submitted a full bid to the Fund, with a decision expected in the New Year.
“Although still in its infancy, the project has already secured the support of the North East LEP, the North East Chamber of Commerce and a range of local businesses.”
She added: “These proposals have the potential to transform South Shields town centre, boosting footfall to the tune of an additional 9,000 people and diversifying away from traditional retail, which we know is no longer enough for the high street to thrive.
“We remain confident that this scheme is a core part of our vision to create a vibrant, sustainable future for the town, making it a great place to live, work, visit and learn.”
Ms Lewell-Buck, who had been championing the project through Parliament, said she was working with project team to ensure funding was delivered to see the project come to fruition.
She said: “I am of course disappointed, but not entirely surprised that this Tory Government chose not to ‘level up’ South Shields.
“However, as my constituents know I have never just relied on the Government to deliver for us.
"As the political lead for this project, I am continuing to work with the developers and the college and will be meeting with the Council soon to explore other avenues of ensuring we obtain the relevant funding to deliver this project.”
Tyne Coast College, of whom South Tyneside College is now part, has been approached for comment.
The college is internationally renowned for its marine school in particular, which sees students from around the globe studying in South Shields for careers at sea.
The marine school originally ran from the building in Ocean Road which is now the Kirkpatrick’s pub.