After finishing recovery from foot surgery in August, Shaw was forced to play for United's U23 side as he worked his way back to full fitness.
Since December, the left-back has enjoyed one of his best runs under Jose Mourinho, having started seven out of United's last ten Premier League matches.
The Portuguese praised Shaw last week, stating that he expected the 23-year-old to sign a new contract and "be a United player for years."
When asked by Tribalfootball about Shaw, Blackmore agreed with Mourinho's sentiment.
"He's definitely good enough to be a United player," said the 1992/93 Premier League winner.
"Unless you're there you don't know what has happened between them.
"For me, the injury was a bad one that has kept him out I'm glad to see him back looking sharp and quick. For me, it's a no brainer you've got to keep him in there."
Clayton Blackmore has a new autobiography out titled 'Red, White & Blackmore', you can purchase it by clicking the link here.