The organisation has teamed up with US buyout firm Blackstone to put forward a takeover proposal for the branches being put up for sale by part-nationalised RBS in order to appease competition concerns.
Wellcome Trust – which specialises in supporting medical research – declined to comment further, but is understood to have submitted a bid earlier this week to UBS, the investment bank handling the auction in time for Tuesday's deadline for initial bids.
A number of would-be buyers are said to be in the running for the network, which comes with the Williams & Glyn's brand name – a sale that could fetch up to 2 billion for RBS.
According to reports, Sir Richard Branson's Virgin Money is among first round bidders, alongside Clydesdale and Yorkshire owner National Australia Bank and Spanish banking groups BBVA and Santander, which bought Abbey and Alliance & Leicester in the UK.
But Wellcome's entry was unexpected, with the group not having been linked to the sale process before today.
It is thought to see the RBS network as a long-term investment opportunity and reportedly comes after recent involvement in bank acquisitions in the US and Bermuda.
Wellcome recently released figures disclosing that its annual charitable spend rose to 720 million after delivering a 5 per cent return on its investments despite the economic woes.
The group – the main source of non-Governmental biomedical research in the UK – said its investment portfolio produced a gain of 580 million in the year to the end of September.
The organisation was set up in 1936 and has an endowment of about 13 billion, making it the world's second richest medical charity after the Gates Foundation.
It was launched after the death of pharmaceutical entrepreneur Sir Henry Wellcome, who left the entire share capital of his company to trustees charged with spending income to further human and animal health.