Arron Banks, funder of the Leave.EU campaign, is considering launching a judicial review.
Mr Banks said changing the law during a campaign was unprecedented, unconstitutional and potentially grounds for a legal challenge.
A Britain Stronger in Europe source said Mr Banks was entitled to spend his money as he wished.
The BBC understands that if there is another glitch before the new deadline of midnight on Thursday the registration period will not be extended again.
Mr Banks, an insurance millionaire, told BBC Radio 4's Today programme: "We've got lawyers that are looking at it at the moment.
"They are tending to say it's unconstitutional because once you've set the rules you can't really change it halfway through, and Parliament really shouldn't be doing this."
'All legal options'
In a statement Mr Banks said: "We believe It is unconstitutional at best and have been advised that with legitimate cause we could challenge this extension.
"We are therefore considering all available legal options with our legal team, with a view to potentially launching a judicial review now and after the outcome of the referendum on 23 June."
Media caption'Once you've set the rules, you can't change them halfway through," says Arron Banks
The official leave campaign - Vote Leave, in which Mr Banks plays no part - has said the government is trying to register as many likely remain voters as possible, but stopped short of suggesting that it would consult lawyers.
A Britain Stronger in Europe source said: "Mr Banks is entitled to spend his money as he wishes. We'll keep pointing out Britain is stronger, safer and better off in the EU - and leaving is a leap in the dark."
The chances of any judicial review succeeding are impossible to assess until the legislation on which MPs will vote on Thursday has been published and studied.
Leave.EU threatened, but did not bring, a judicial review against the Electoral Commission's decision to make Vote Leave the designated lead out campaign.
Source: BBC NEWS
