Harris' offer, made public on Monday, comes after Portsmouth's administrators PKF confirmed earlier this month they were considering a bid he was fronting.
The Football League responded then by announcing the south coast club would be expelled if the Pompey Supporters' Trust - PKF's preferred bidder - was not successful.
Trust spokesman Colin Farmery said fans had no interest in Harris' offer, in which 15% of shares will be allocated free to a group made up of supporters who have donated funds to PST, season-ticket holders and hospitality clients.
Farmery said: "Why would we be interested in 15% when we are just about to take a 100% stake in the club?
"It is curious timing to say the least from Mr Harris with the Football League having made it quite clear that our bid is the only one that can be considered.
"Mr Harris seems to think he has still got a bid but he hasn't. Our bid is literally about dotting the i's and crossing the t's."
The Trust expect to move a step closer to acquiring the club on Thursday when a court hearing will set a final date for the valuation of Fratton Park to be heard, followed by a high court date at which the Trust expect to be given the right to take over the club.