The Independent Group (TIG) of MPs is holding talks with the Electoral Commission about becoming a political party.
Chuka Umunna, who acts as TIG spokesperson, said on Tuesday “we think people want an alternative”.
“If you want to present an alternative you have to become a party,” he said.
“We have been absolutely overwhelmed by the tens of thousands of people who have signed up to our website, who have shown support for what we are doing and want to see an alternative, to build an alternative.”
Speaking as he arrived at the Electoral Commission HQ in central London, he added: “We aren’t a political party but quite clearly there is an appetite for a new one, so we are here to discuss with them what that involves.”
Umunna was joined at the meeting by former Labour MPs Gavin Shuker, Ann Coffey and Chris Leslie and former Tory Heidi Allen.
Eight ex-Labour MPs and three ex-Tory MPs set up the breakaway group in protest at the direction of their former parties.
All of the MPs are ardently pro-EU and support a second Brexit referendum.
Labour has demanded the MPs submit themselves to immediate by-elections - something TIG has rejected.