Parliament's Intelligence and Security Committee must remain "non-partisan", its former chairman has told the BBC.
Boris Johnson has suggested ex-cabinet minister Chris Grayling take over the role - one of five Tory MPs he has picked to form the nine-member body.
But ex-chairman Dominic Grieve said the PM should not "be seeking to tell the committee who should be the chair".
But it has not met since the 2019 general election, the longest hiatus since it was set up in 1994.
Opposition parties have previously accused the government of trying to escape scrutiny by delaying the committee's formation.
Mr Grieve, himself a former Conservative cabinet minister, told BBC Radio 4's Today programme: "The whole point about this committee is it is non-partisan.
"The prime minister nor anybody should be seeking to tell the committee who should be the chair. It is for the committee to decide under the statute which sets it up."
The House of Commons - in which there is a Conservative majority of almost 80 - votes next week on whether to approve the government's nominations, which also include two Labour MPs and one SNP MP.
A member of the House of Lords will also sit on the committee. The government has chosen Labour's Lord West of Spithead, a former security minister.
'Must be respected'
The Conservative members put forward by Downing Street are believed to be Mr Grayling, John Hayes, Julian Lewis, Mark Pritchard and Theresa Villiers. A majority on the committee for the party would mean its MPs can pick the chair.
Mr Grieve said: "I don't have a view for who the right chair should be, apart from the fact I'm absolutely clear in my mind it should be a matter for the committee and that the committee should not be put under party political pressure as to who the chair should be."
He added: "The chair should be somebody who is respected on a cross-party basis."
The Labour committee members are set to be Kevan Jones and Dame Diana Johnson, while the SNP will have one representative - Stewart Hosie.
The results of the Russian inquiry, which began in November 2017, were passed to Mr Johnson in October last year.
A government spokesman said the prime minister had approved the report for publication in December.
But it was up to the committee, whose previous members investigated and wrote the report, to publish it.