Press Association Sport understands the Australia international, who will be 33 in December, has already turned down a 16 million dollar (£10.3million) three-year deal from an unnamed club in the oil-rich nation.
He has been linked to Al Nassr but is also reportedly attracting interest from other clubs in the region as well as China.
Cahill has two years remaining on his contract at Goodison Park and is happy at the club he joined in 2004 but would consider a move overseas.
Also Everton, who are keen to re-sign Steven Pienaar from Tottenham after the South Africa international impressed on a loan spell in the last four months of the season, would most likely look to cash in on Cahill should they receive a good offer.
It is understood Cahill is weighing up his options and would consider a move to play in the Middle East.
The midfielder is currently on international duty with Australia in Oman, where the footballoos begin their final phase of qualifying for the World Cup on Friday before hosting Japan in Brisbane on Tuesday.
Cahill is currently one of Everton's longest serving players, making 278 appearances and scoring 68 goals.