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".

McIlorum, 28, went off on a stretcher after a tackle on Broncos half-back Anthony Milford and went to hospital.
The Leeds-born England international has played 220 games for the Warriors.
"Micky could be out for six months," Wigan coach Shaun Wane told BBC Radio 5 live sports extra. "He's playing rugby league and these things happen."

The Travel Photographer of the Year Awards is staging the outdoor exhibition at Princes Dock Street.
The show is part of the second season of Hull's year as UK City of Culture.  Entitled Roots and Routes, it aims to celebrate Hull's role as a major port and its international connections.
The awards began in 2003 and accept entries from amateurs, semi-professionals and professionals.
Read more about this and other stories from Hull and East Yorkshire
See some of the winning entries
The photographs on display include a selection of winning entries from the 2016 competition.
Entrants from more than 120 countries entered the competition and photographers from 21 countries featured among the winners.
Martin Green, chief executive and director of Hull UK City of Culture 2017, said: "Our Roots and Routes season is all about celebrating Hull's global connections and its place in the wider world.
"This exhibition will give people in Hull the opportunity to see unique images of some of the planet's most famous and recognisable places along with exposing them to some far-flung and unfamiliar locations and sights."
The photographs will remain on show until 30 June.
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.
[NEXT_CONCEPT]
Wigan hooker Michael McIlorum is facing a six-month lay-off after sustaining a suspected broken ankle in Saturday's World Club Series defeat by Brisbane.
[NEXT_CONCEPT]
A free showing of award-winning travel photographs has opened in Hull.