July 3 (Reuters) - Private-equity firm New Mountain Capital has submitted a buyout proposal for healthcare services provider R1 RCM in an all-cash deal, valuing the company at nearly $6 billion as per a filing on Tuesday.

New Mountain Capital submitted an all-cash proposal to acquire all of the Utah-based company's outstanding shares it does not already own for a proposed price of $13.25 apiece.

R1 RCM did not immediately respond to a Reuters request for comment.

In February, a group of R1 RCM's investors led by New Mountain had

submitted a draft proposal

to acquire all of the company's outstanding shares not owned by the investors for a proposed price of $13.75 per share in cash.

New Mountain, however, said on July 1 that it was no longer interested in the joint proposal for the take-private deal.

The current valuation of the healthcare service provider stands at $4.59 billion, as per LSEG. Its shares have gained a little over 5% so far this year.

According to the filing, R1 RCM has not provided any response to the private equity firm.

(Reporting by Pritam Biswas in Bengaluru; Editing by Krishna Chandra Eluri and Alan Barona)