The Leeds striker has a year still to run on his contract at Elland Road but has been linked with a return to Bramall Lane following the appointment of Nigel Adkins as Blades manager.
Sharp played for Scunthorpe under Adkins, who later signed the 29-year-old for £1.8 million during his time in charge at Southampton.
“I think it’s an obvious one,” said Morgan at a press conference to promote his testimonial against Newcastle on July 26.
“The gaffer’s had him at Scunthorpe and also Southampton.
“Sharpy has made no secret of the fact he’d love another shot at coming to play for the club.
“I know Billy personally and I think he’d love nothing better than to come because the two times he’s had here I think he feels he’s not had the opportunity to show the real Billy Sharp.
“People have always commented that he’s struggled here in his two spells, but been a hit everywhere else.
“He’s gone and scored goals. Probably, if you were to ask Billy like you’ve asked me, when was the best spell you had as a player, well it’s been under Nigel.
“It is an obvious one to put out there, but genuinely there’s been no talk between me and the manager about Billy.
“But it wouldn’t surprise me because of the relationship they have as manager and player and let’s face it, Billy’s track record of scoring goals.
“The two spells he’s had he’s never really showed the real Billy Sharp.”
Morgan, appointed Under-21s coach following Adkins’ recent appointment, has spent 12 years with the Blades as a player and coach since signing from Barnsley in 2003.
He skippered the Blades to promotion to the Premier League in 2006 and made a total of 247 appearances for the club.
His testimonial kicks-off at 1pm at Bramall Lane on Sunday, July 26, with all proceeds being donated to three charities – Weston Park, Bluebell Wood and the Gary Speed Trust.