Boles who opposes a no-deal scenario and has led calls for Brexit to be delayed and softened said he had thought about being an independent MP but decided to stick with the Conservatives at Westminster level for now.
There have been suggestions that Boles could be the next MP to join TIG, following Anna Soubry, Heidi Allen, and Sarah Wollaston, who quit the Tories last month to join the anti-Brexit House of Commons grouping.
Last month, he described the eleven MPs who quit the Conservatives and Labour to join TIG as "good people" and that he could "understand completely" why they had chosen to ditch their parties to form a new group.
However, TIG's chief spokesperson Umunna played down talk of Boles joining TIG on Monday.
He told Business Insider: "I have not detected that Nick is a great reformer in political terms. Would he want to change our voting system? Upend the antiquated way in which things play out in parliament? I'm not so sure."
"I don't know enough about Nick's politics in detail but I'd say the same about George Osborne. He is sometimes described as centre-right but I think that stretches the description somewhat.
"Economically, Osborne is pretty liberal and dry in Thatcherite terms. Nick probably is too."
Umunna was expanding on remarks he made earlier in the day told an event in central London, where he said: "I'm not sure that Nick shares the same progressive valuesthat we do or progressive politics."
The former minister told BI: "There is probably more common ground around social values and issues to do with equality ... but let's have a conversation.
"I never got the impression that Nick's values were particularly progressive in the broader sense of that word."
TIG aims to be a party by the end of the year and claims to be in talks with MPs across the Commons about potentially joining. No more MPs have defected since eight former Labour MPs and three ex-Tories defected last month.
However, disgruntled MPs in the two main parties who could potentially walk away are not expected to make moves until the next few weeks of the Brexit process have played out.
SEE ALSO: Theresa May could cancel plans to hold a third vote on her Brexit deal this week
