Reports on Sunday suggested United manager David Moyes had been given the go ahead to chase Bale and former Old Trafford favourite Cristiano Ronaldo.
Moyes played down the reports during a press conference, but said the club were looking at signing the 'best players'.
And Yorke thinks the 23-year-old, who was voted both the football writers' and players' player of the year last season, would represent a 'fantastic' signing for his former club.
Talking to reporters at a youth coaching clinic in Gosford, hosted at reigning A-League champions Central Coast Mariners, Yorke said: "We've still got a lot of quality within the Manchester United team at this present time, but the manager is always looking to strengthen.
"People like Gareth Bale – in terms of what he's done, the player he has become over the years. He would be a fantastic player to join Manchester United."
United missed out on signing Thiago Alcantara, whose move from Barcelona to Bayern Munich was confirmed on Sunday, but Yorke thinks Ryan Giggs can help fill the void left by Paul Scholes' retirement.
The 39-year-old may operate alongside Michael Carrick in the centre of midfield, and Yorke was full of praise for the Welshman.
"He's the best. You just have to look at what he brings – his personality, his presence, his aura on the football pitch and on top of all that he's a fantastic athlete," Yorke said.
"He's a first-class player and he's continued to do well."
Yorke also believes Aston Villa striker Christian Benteke will be tested in his second season in the Premier League after scoring 19 goals during his debut campaign.
Benteke requested a transfer from Villa – another of Yorke's former clubs – on July 8, with Goal understanding that Chelsea are preparing an offer for him, though Tottenham are unwilling to meet Villa's asking price.
"He certainly burst onto the scene this year. It'd be interesting to see how he gets on this particular year because the first year is always the easy bit," he said.
"He looks an outstanding prospect and of course there's a lot of interest in him at this present time. He certainly caught the eye."