Premiership Rugby is auditing its clubs' grounds to look for suitable venues to host rugby union's restart.
Following government guidance, rugby's governing bodies are continuing to plan for the sport's safe return.
With nine rounds of the season left, the preference remains to stage whole rounds of games at one venue for safety and logistical reasons.
However, Twickenham and Wasps' Ricoh Arena - while not ruled out - do not meet all the criteria.
The BBC understands these criteria are:
While Twickenham was initially considered to be the best option to host the games, it is costly to run and is currently being used by the NHS. Meanwhile the Ricoh Arena in Coventry lacks nearby training facilities.
Hosting the matches at a neutral ground outside of the 12 Premiership venues has been considered, but it is understood this is unlikely as the rugby authorities want control of the venue throughout the week for safety reasons.
The power-brokers of the English game meet on Thursday for further discussions, with the RFU warning there is "still significant work to do" and that player and staff welfare will "be at the heart" of decision-making.
The Rugby Players' Association added that "no players, coaches or support staff will be at significant risk when rugby returns" while Premiership Rugby boss Darren Childs said "our job is now to find a safe way for one of our greatest national sports to thrive".
A return date in early July remains the target, although the BBC has learned that the weekend of 27 June has also been mooted.
Some Premiership clubs are set to begin a phased return to training next week, with Harlequins scrum-half Danny Care telling the Rugby Union Weekly podcast that the players are "desperate" to get back playing if safe to do so, and that "rugby needs to come back" given the perilous financial predicament many clubs are facing.
The majority of clubs have pushed through a 25% wage cut on their players, which is set to stay in place for the foreseeable future, with full crowds - and therefore full revenues - not expected potentially until 2021.
However, there is concern over how the return to training affects players who are out of contract at their current clubs at the end of June.
Even though the season is yet to be completed, players are still set to move clubs by 1 July, opening up the possibility of players returning to train at a club for a short period while knowing they won't play for them again.