MOSCOW (Reuters) - Russian presidents could be made senators for life when they leave office under a proposed reform, a senior lawmaker said on Tuesday, a status that would give them immunity from prosecution.

The initiative, drawn up by a government commission, follows sweeping changes to Russia's political system proposed last month by President Vladimir Putin.

Putin's proposals, which were accompanied by a government reshuffle, would shift power away from the presidency and were widely seen as being designed to help him extend his grip on power after he leaves the presidency in 2024.

The lower house of parliament backed the changes in a preliminary vote last month. The commission's proposals will also be put to a vote.

Among them is a suggestion presidents become lawmakers for life in the upper house of parliament once their terms in the Kremlin end or they resign, Pavel Krasheninnikov, the working group's deputy head, said, Interfax news agency reported.

Under Russian law, lawmakers in the lower and upper houses of parliament are immune to criminal prosecution.

Krasheninnikov said the idea had been put forward by members of the working group and was based on their study of upper houses of parliament in other countries. He did not say the move was meant to shield former presidents from criminal prosecution.

He said it would allow Russia to tap into the "colossal experience and knowledge" of former presidents.

The commission has already put forward an array of other proposals, including one that would change Putin’s job description to Supreme Ruler.

Before they become law, the constitutional amendments must be approved by the lower house of parliament in two further votes before being voted on by the upper house, examined by regional parliaments, and then signed by Putin.

Putin has said the changes would be put to a nationwide vote, but it is unclear when that could take place.

(Reporting by Gabrielle Tétrault-Farber and Tom Balmforth; editing by Philippa Fletcher)