The Tottenham Hotspur Supporters' Trust fears the club's identity risks being severely damaged if the wrong groundshare option is taken for the 2017-18 season.
Spurs are assessing all alternatives for a temporary home - including Wembley, the Olympic Stadium and stadium:mk - after announcing a delay in the construction of their new stadium.
Spurs plan to build a 56,250-capacity venue next to the existing White Hart Lane ground, which holds around 36,240.
In July the club overcame a major hurdle after the government approved a compulsory purchase order allowing building work to begin. However, seven years of negotiations with one landowner are still to reach a satisfactory conclusion, resulting in the delay.
A High Court challenge has resulted in a revised construction programme, with the shortest build time meaning Spurs must leave White Hart Lane to allow the new stadium to be built adjacent to the present site.
However, the new ground will not be ready in time for the start of the 2017-18 campaign and a short-term temporary measure must now be identified.
THST board member Martin Cloake told Press Associaition Sport on Thursday that Wembley would be considered the preferred option but the Trust has issued a statement on its website outlining its main concerns about a move to a temporary home and the impact such a decision will have on fans.
"The board of the Tottenham Hotspur Supporters' Trust is understandably concerned to hear the latest announcement from the club regarding delays to the building of a new stadium," the statement read.
"While we cannot, for obvious reasons, comment on the details of the legal process around the High Court appeal, we find it surprising that negotiations between the club and one business have continued for seven years without resolution."
Although accepting that a move may be beyond anyone's control, THST also laid out issues it worries could risk longer-reaching changes to its club.
"While the Trust is pragmatic about the need to move from White Hart Lane for one season, the prospect of moving from north London raises a number of issues for supporters, the local community, and the club's identity.
"For the supporters, there are serious issues over the logistics and expense of travel to home games. For the local community, which is depending upon the stadium project as a catalyst for regeneration, there are serious economic implications. We believe the cost of such a move to the local economy needs to be seriously considered.
"Moving away from the area threatens serious damage to the identity of a club which has always played in north London. We would like greater transparency as to why the option of playing at White Hart Lane, the option which would benefit N17 the most, is apparently now no longer available.
"Our greatest concern is that, once the club moves for one season, it is but a short step towards moving for two seasons, or more.
"When the club's current board tried to move us to Stratford, Tottenham Hotspur supporters showed their fierce opposition and we would urge the club to learn the lessons from that episode. A football club divorces itself from its community and identity at its peril."
Meanwhile, former Tottenham striker Clive Allen has identified the Olympic Stadium as a perfect temporary home.
The focal point of the London 2012 Games is currently undergoing building work to become a football-friendly venue, with West Ham taking over as long-term anchor tenants from the start of the 2016-17 season.
But Allen still feels the east London venue would work out well for Spurs.
"Although the MK Dons stadium is a fantastic place, I think it's just a bit too far," he told talkSPORT.
"The Olympic Stadium would be perfect. There was interest from the club in terms of moving there anyway.
"I can't see a reason why (West Ham would oppose the move). They will move in there and make it their new home but there are so many teams throughout Europe who share their grounds.
"I can't see it would be a major problem that on alternate weeks Spurs can use it."