Digital infrastructure minister Matt Warman said if there was demand for more transparency then it was “right” that such a register be considered.
It comes after the Government was plunged into “cash for access” row following accusations levelled at the Conservative Party chairman.
The Financial Times reported Ben Elliot, the Duchess of Cornwall’s nephew, developed a club in a bid to connect Tory supporters with senior figures, adding that regular meetings and calls have been held with Prime Minister Boris Johnson and Chancellor Rishi Sunak.
He has also been accused of selling wealthy clients access to his uncle the Prince of Wales.
Asked if the Government would consider publishing a list of who the PM and the Chancellor meet on a regular basis, Mr Warman told Times Radio they would “comply with the law as it stands”.
He said ultimately every meeting and donation is declared in the way that is “required by the rule”.
But pressed on the issue and that the Labour Party could be included, he replied: “I think what is a sensible approach is to have, as you say, one rule that goes across all political parties.
“That will be quite a big change and if it’s something that there is demand for, of course, it is right that people consider that.
“But, right now, the important thing has to be to make sure that everything is declared in line with the rules, and that’s what we do.”
It comes after Labour Chairwoman Anneliese Dodds called on the Tories to publish a list of ministers who have met major party donors through the secretive club.
Ms Dodds wrote to Conservative co-chairman Amanda Milling demanding they “come clean” about the level of access afforded to financial backers as part of the so-called “advisory group”.