The owners of the Ricoh Arena were prepared to let the club play there rent-free this season but City have elected to pursue a deal with the League Two outfit.
The deal would see City pay to hire the ground, which is a 68-mile round-trip from Coventry, on matchdays only.
Coventry had been looking at groundshare options after becoming embroiled in a rent dispute with the owners of their stadium, Arena Coventry Ltd (ACL) last year.
The move to Northampton looks likely to go ahead though despite the opposition of supporters' groups, who are vehemently opposed to the club leaving their home city.
A Sky Blue Trust spokesman said: "We know supporters overwhelmingly oppose any move out of Coventry and the Trust's view is simple: it is unthinkable that CCFC play home games outside the city in which we were founded and is our home."
The club have been in administration since March and, despite being bought by Otium Entertainment Group last week, they will remain so until they arrange a Company Voluntary Agreement (CVA) to pay creditors.
A statement from Paul Appleton, joint administrator for Coventry City FC Limited, read: "The offer made by ACL to allow the club to play at the Ricoh was dependent on Coventry City FC Limited remaining in administration. That is obviously still the case.
"However, as I've stated on many occasions, including my press release last Thursday following the completion of the sale of the Company's assets, Holdings employs the players.
"There are insufficient assets in Limited to employ either a team of players, associated coaching staff or commercial operations to take up this offer.
"I'm somewhat surprised to hear ACL claim they have heard nothing from me on this matter given their solicitor was fully briefed on the reasons behind the decision not to take up their offer by my legal team on June 12."
However, a Ricoh Arena spokesman hit back, saying: "The way the fans have been treated by the club's owners is utterly cruel.
"There is no reason for the club to leave the city of Coventry. We trust that the Football League, as an organisation which holds the passions and interests of fans close to its heart, will not sanction this proposed move under any circumstances."