The board of PSSL is also axing its investment management agreement with private equity firm Pollen Street Capital, co-owner of British challenger bank Shawbrook, due to governance issues, it said in a statement.
The possible 900 pence per share offer for PSSL, which invests in corporate loans and peer-to-peer debt, represents an 8.7% premium to Monday's closing share price.
Waterfall has received an irrevocable undertaking from Invesco, the investment trust's largest shareholder, to support the offer, the firms said.
PSSL's shares jumped on the news and were trading up 6.5% at 882 pence at 1016 GMT, at the top of the FTSE 250 index.
PSSL's board also said it was terminating the agreement of investment manager Lindsey McMurray, the CEO of Pollen Street Capital, "in light of what the board considers to be, and has been advised are serious, repeated and ongoing breaches of the manager's obligations".
The PSSL board said the investment manager did not provide it with sufficient information for Waterfall to carry out due diligence and published information about the company's dividend without its approval.
Pollen Street Capital said in a statement it was "deeply disappointed" with the decision to terminate the agreement.
It said it was concerned about the amount of information which the PSSL board wanted to share with Waterfall and with the operational restrictions sought by the board following the Jan. 8 offer.
By Carolyn Cohn