Barnsley Council says it is "shocked and dismayed" to read the Championship club is considering whether to move out of their Oakwell stadium.
Barnsley are in dispute with the council over attempts to buy Oakwell.
Barnsley Council have 50% ownership of the stadium, with the Cryne family retaining the other 50%.
It has been claimed the club's owners want to improve Oakwell but are unwilling to do so until they have ownership of it.
A Daily Mail report
said Barnsley may look to play elsewhere because of the lack of a deal.
The club have not commented on the row, or suggestions their options are as far afield as Lancashire, even though there are a number of clubs far closer who have relatively new stadiums.
However, the council are keen to play down any suggestion of a row and insist they "will do all they can" to keep the club at Oakwell.
Leader of Barnsley Council, councillor Sir Steve Houghton, said: "We're shocked and dismayed at the comments regarding the potential relocation of Barnsley Football Club.
"For the last 133 years, Barnsley Football Club has been a significant part of our borough, and we'll do all we can to make sure professional football is maintained in Barnsley."