In a statement, the firm said it was in advanced talks with its authorised corporate director to transfer its top performing funds to a new investment adviser.
The Somerset Asia Income and Somerset Emerging Market Dividend Growth funds, along with their key investment team, are seeking to transition to a new investment adviser but would retain the existing fund and third-party infrastructure.
Somerset Capital loses two-thirds of assets as SJP severs ties - reports
"If agreed, this will ensure the seamless continuity of these funds and their managers, while positioning them for continued growth," the firm said.
Somerset was founded in 2007 by Rees-Mogg, Johnson and Edward Robertson, who remains at the firm and manages its Global Emerging Markets fund.
Last week, the FT reported the firm had lost over two-thirds of its assets under management as SJP severed ties with it.
The termination of the relationship was described as a "blow" to Somerset and "called into question its future".
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The firm went from managing $3.5bn in assets at the end of October to about $1bn, after SJP transitioned about £2bn away from the firm on 20 November.
Oliver Crawley, partner at Somerset Capital, said: "It has been a privilege to manage capital for world-leading institutions and clients for over 16 years. I am incredibly proud of all we have achieved in that time through the hard work and skill of our dedicated team."
Crawley expressed confidence in the prospects of the departing funds: "The current teams have delivered strong performance for their investors and continue to do so. We hope a transition can be secured which we believe will give the funds a bright future."