Feb 26 (Reuters) - A group of R1 RCM's investors is considering taking the healthcare services provider private, according to a regulatory filing on Monday, sending shares of the company up as much as 31%.

The investor group, led by equity firm New Mountain Capital, said it had submitted a draft proposal to acquire all of the Utah-based company's outstanding shares not currently owned by the investors for a proposed price of $13.75 per share in cash.

Coliseum Capital Management LLC, one of the five largest shareholders, in an open letter to the company's board said it believes the offer "significantly undervalues" the company.

The shareholders said the board should "require a materially higher price, or reject the offer and stay the course as a public company."

New Mountain Capital and its affiliates also disclosed that they have been in discussions with investment vehicle TCP-ASC regarding the proposed take-private offer.

TCP-ASC is jointly owned by TowerBrook Capital Partners and Ascension Health Alliance.

New Mountain Capital holds a 32.43% stake in R1 RCM, while TowerBrook has a 29.64% stake, according to LSEG data.

"While there is not final agreement on terms as of this date, these discussions remain ongoing and there is active dialogue," the investor group said in a filing.

According to the filing, RCM is discussing the request and there is no final agreement on terms. R1 RCM did not immediately respond to a Reuters request for comment. (Reporting by Christy Santhosh, Bhanvi Satija and Sriparna Roy in Bengaluru; Editing by Maju Samuel)