The offer said by analysts to have come from a large Indian oil company, is believed to be at around the 350p level.
Gulfsands’ board, advised by Royal Bank of Canada, is said to be seeking an offer over 400p.
Schroders has a 21.7 per cent stake in the Aim-listed company, meaning any deal would need its approval.
Shares in the Syrian-focused explorer, which also has assets in the Gulf of Mexico, surged 20 per cent to 312.5p, giving the company a market cap of £375.2m.
Gulfsands is currently working on exploration and appraisal activity around its 17,000 barrels per day Khurbet East field on its 50 per cent owned and operated Block 26 in Syria.