However, the Doonhamers are not interested in the terms offered by their First Division rivals.
"There will be no deal until the price is right - he's not leaving us for two bob and a doughnut," manager Kenny Brannigan told the club website.
"Bob's a born leader and that's why I made him captain. He's still got nearly a year of his contract to run.
"They want him for half the price and even offered four players in return - and one of those was (former Queens player) Eric Paton."
Glasgow-born Harris began his career at Clyde before signing for Queens in 2007.
Harris himself insisted he would not let the speculation affect him.
He's not leaving us for two bob and a doughnut
Queen of the South manager Kenny Brannigan
"There's been an awful lot of talk but I try and not let all the speculation get to me," he explained.
"I still have a whole season's contract in front of me and I'm quite willing to see it out here at Palmerston.
"I'm a Queen of the South player and I'll give the club 100%."
Source: BBC Sport
Source: BBC Sport