McLeish was speaking after watching his side reach the fourth round of the FA Cup with a 3-1 victory at Bristol Rovers.
England striker Bent, 27, who joined Villa from Sunderland a year ago, has been linked with a move away, with Liverpool reportedly among the favourites, and he played in Saturday night's win at the Memorial Stadium.
McLeish has insisted that the player will not be sold, but rumours have persisted.
However, the former Birmingham manager, who is also hopeful of completing a short-term loan deal for Los Angeles Galaxy striker Robbie Keane within the next 48 hours despite what he described as "red tape" holding up the move, says that no-one he has spoken to, including Dalglish, has expressed an interest in Bent.
Of the continued speculation, McLeish said: "It's not frustrating, it's just the transfer window.
"People like to speculate and use social networking sites and they are having a field day.
"If there is anybody out there that wants him they certainly haven't contacted me and Darren has said on the record he wants to stay at the club.
"Whenever I have asked anyone outside the club I've been told flatly 'No'.
"I have spoken to Kenny and he said there was nothing in it."