Birmingham International Airport has turned down a £30 million offer to buy rival Coventry Airport.
Board members of BIA discussed a possible deal last month after being approached by Coventry Airport's owners, TUI.
They were given a matter of days by TUI to decide whether to submit a bid.
Although the matter has not been put formally to a board meeting, representatives of the seven West Midlands District Councils, which retain a 49 per cent interest in BIA, believe the price-tag is too high.
It is understood that BIA might be prepared to offer about half of the asking price.
Coventry Airport, which controversially began operating low-cost passenger flights by Thomsonfly in April 2004, has been at the centre of a bitter planning row over a new terminal and 4,000-space car park.
Plans for the terminal, capable of dealing with two million passengers a year, were finally given conditional approval by Warwick District Council last month.
Shortly before Warwick's decision, BIA was asked whether it would be interested in joining other prospective bidders in submitting an offer for the lease of Coventry Airport.
Officials of the Birmingham Airport company called
board members over a weekend to ask their opinion.
TUI agreed to allow serious bidders an opportunity to examine the airports accounts and financial forecasts. Those taking up the offer were asked to sign a confidentiality agreement.
BIA board members who were asked for their views expressed fears that substantial investment would be
required to modernise Coventry Airport and it would be years before the purchase would yield any profit.
Ken Taylor, the leader of Coventry City Council, who is a BIA board member, said: "There was consideration given to buying Coventry Airport but I think we are backing off slightly at the moment.
"There is no reason to put money into something that is not going to make a profit for a long time. You would be talking about spending tens of millions of pounds if you wanted to develop Coventry Airport."
Another BIA board member, who did not want to be named, cautioned against getting involved in a bidding war that could push up the cost of buying Coventry Airport beyond a realistic level.
However, there are also concerns at the possibility of Manchester Airport emerging as a prospective buyer.
The ownership of BIA is split among the seven West Midlands district councils, which have 49 per cent of the shares, Aer Rianta with 24.1 per cent, Macquarie Airports Group 24.1 per cent.
The remaining 2.75 per cent takes the form of an employee share trust.
A spokeswoman for BIA said: "The airport company will not comment on speculative reports."
Coventry Airport is known to have been the subject of a number of speculative bids since being acquired by TUI.
Bill Savage, managing director of Coventry Airport, refused to comment on a possible bid by Birmingham.
However, he added: "TUI's commitment to Coventry Airport is 100 per cent and it will remain so if the airport lease is sold to another operator, or part of it is."