Obiang is the subject of interest from Italy after Fiorentina offered £5m last week.
Obiang joined the Hammers from Sampdoria last summer but made just 11 Premier League starts in his first season with the club as he found opportunities restricted by the good form of the likes of Mark Noble, Cheikhou Kouyate, and Dimitri Payet.
With Slaven Bilic having added defensive midfielder Havard Nordtveit to his squad this summer, it looks as though Obiang may face an even bigger struggle to hold down a first-team spot this term.
As a result, West Ham are thought to be open to the idea of selling the Spaniard, and the majority of the interest seems to be coming from Italy.
It was reported earlier this month that Fiorentina had launched an offer worth around £5 million for the midfielder, but the Irons are not thought to be looking to stoop so low in their valuation.
Now, Tuttosport reports that Torino have also enquired about signing Obiang, with manager Sinisa Mihajilovic keen on reuniting with the man who played under hime for two years at Sampdoria.
The report claims that West Ham are holding out for around €7.8 million (£6.75 million) for the midfielder, which is significantly more than what was offered in the first instance by Fiorentina.
It remains to be seen whether their valuation of Obiang will be met in the next fortnight, or whether he will remain at Hammer for the time being.