A Lewisham Council cabinet meeting, which was set to confirm a compulsory purchase order (CPO) for the land, has been postponed until February.
The Lions have played in Lewisham since 1910 and at The Den since 1993.
"I can't rule out relocation in the event the CPO went through," Kavanagh told BBC Radio 5 live.
Lewisham Council aims to regenerate the land around Millwall's ground in conjunction with property developer Renewal as part of the 'New Bermondsey' scheme, which proposes to create 2,400 homes, community facilities and a new overground station near the stadium.
Kavanagh says Millwall "actively" support regeneration of the area, but the League One club want to be involved in any scheme as the current CPO would affect the future of their academy and the Millwall Community Trust (MCT).
"We are calling for regeneration and development but we don't want to feel we are not important in this," Kavanagh added.
"If we are treated in such a manner that this CPO goes through and we are not at the heart of the proposed redevelopment, then we have to consider what we do.
"I have to look at every single angle to make sure the commercial viability and the long-term future of the club, and its community trust, is well served where we live."
Lions supporters have been vocal in their opposition to the CPO, with an online petition against the proposals gathering more than 27,000 signatures.
Tim Farron MP has been among the politicians to speak out about the plans, with the leader of the Liberal Democrats saying it would be "heartbreaking" for Millwall fans and the local community if the club were forced to move.
Mayor of London Sadiq Khan also "wholeheartedly supports" Millwall remaining in Lewisham.
On Monday, Kavanagh wrote to the council seeking talks about the "critical issues" surrounding the CPO, which the council said were a factor in the postponement of Wednesday's meeting.
"There has been an ongoing exchange of correspondence between the council and Millwall FC over the last few weeks," a statement from Lewisham Council said.
"A little more time is needed to complete this, and so the mayor and cabinet is not in a position to reconsider the decision.
"We are asking Millwall to provide outstanding information by 23 January as we intend to reconsider and make the decision in February."
The council has previously stated it is "very supportive" of Millwall and that its ability to operate at The Den "must and will be protected".
Millwall would have to consider a move away from London if land around The Den is sold to developers, according to chief executive Steve Kavanagh.