Posh this summer tried to sign Wells, whose 26 goals last season helped fire the Bantams to the Capital One Cup final and promotion to League One.
During a Q&A session set up by MacAnthony on Twitter on Monday afternoon he stated that he offered the Yorkshire club more than the B£1.1million paid to Crawley for Tyrone Barnett 18 months ago but it was turned down.
"We made a club record bid but in fairness to Bradford they don't need the money, so good for them," MacAnthony tweeted.
MacAnthony also suggested that Peterborough's search for a new striker is becoming frustrating.
The start of the new season is just five days away and Posh are yet to replace Dwight Gayle following his move to Premier League newcomers Crystal Palace at the beginning of July.
MacAnthony added on the social networking site: "Nobody wants to sell us a striker. All afraid we might sell them for many millions in 12 months time and they will look daft.
"There is not a lot i can do if clubs won't sell us their players or if they want money that would bankrupt us. We are working 24/7 to acquire talent if it's available.
"We had three main targets. One is dead in the water but we're still trying on the other two. One is a gem that nobody would think about."
- Sports & Recreation