Gregory has been linked with string of clubs in England and Scotland
Gregory, who arrived in the capital from non-league Halifax Town two years ago, currently has a year to run on his deal, prompting talk he could be sold on following Millwall's failure to secure promotion.
However, according to Harris the League One side are protected.
"There has been no contact from anybody. Lee is not for sale," the 38-year-old told South London Today.
Harris is a former Lions striker himself
"Lee is under contract for another 12 months and the club have an option to extend the contract for another year."
Gregory scored 26 goals in all competitions last season, adding to the eight he scored the previous campaign at Championship level.
Gregory scored 26 goals in total last season
Understandably, his form his said to have attracted several suitors, with Hull City and Brighton & Hove Albion also mentioned in the report, though Harris added: "It only takes one person to say 'he’s linked with a club' and then it’s 'he's going'.
"I’ve not heard anything on these clubs. It’s new to me."
Sheffield-born Gregory, who once partnered England striker Jamie Vardy at Halifax Town, may be keen on a move north should any offers materialise.
However, a move to Wednesday would likely be a tough sell for the boyhood Sheffield United fan.
England star Vardy is a former teammate of Gregory