SRG's tailoring and young-fashion businesses Chester Barrie and Woodhouse are understood to have been formally put up for sale, but Gresham is also thought to be unofficially touting the Suits You, Young's Hire and Racing Green businesses.
One source close to the situation said: 'We were approached and told we could make an offer for any part of the business piecemeal, or table a bid for the entire group.'
SRG is the latest in a long line of private equity deals to turn sour. Gresham bought SRG in 2005 for about£30 million, but sales are thought to have since plummeted amid massive price deflation. A sale could prompt a major shake-up of the menswear market.
Rival menswear business Moss Bros has been tipped as the favourite to buy SRG's 80-store chain Suits You - although it has yet to submit a bid. However, it is understood to have put in an offer for Chester Barrie. Moss Bros is thought to be interested in the Young's Hire and Racing Green businesses as well.
However, Moss Bros issued a profit warning in January and is about to embark on a full strategic review of its business, which could delay a bid for SRG.
A source close to Moss Bros said: 'Buying Suits You may add strategic value to Moss, but I'm not sure of the timing. The board is about to embark on a full review to get a clearly defined and focused view of the future and how it can get growth over the next three years.'
Sources in the market said that buying Suits You would bring cost savings and bolster buying power at Moss Bros, but warned that it would be risky given the levels of debt and product problems that both chains were facing. There are also a significant number of store overlaps.
Menswear supplier BMB and Austin Reed have also been mooted as possible buyers.
Despite being open to offers, Gresham is believed to have secured additional cash to safeguard SRG's short-term future if an acceptable offer for the group is not forthcoming.
Acting chief executive Anton Woodhouse, who joined the business following the departure of Adrian Wright earlier this month, is understood to have met with the board to formulate a recovery strategy this week. The former Peacocks director is planning to drive Suits You further into the value and discount suiting markets, while the Racing Green brand is thought to have potential overseas.
No one from Gresham or SRG was available for comment.