The 53-year-old Portuguese, out of work since being axed by Chelsea in December, has been widely linked to Manchester United where Louis van Gaal has spent most of the season under almost constant siege.
Mourinho, speaking to Sky Sports News on the sidelines of Saturday's world heavyweight boxing title clash between Anthony Joshua and Charles Martin in London, confirmed that Syria had sounded him out.
"They (The Syrian FA) published (the offer) on their website the letter they sent to my agent," he said.
Syria recently sacked coach Fajr Ibrahim and have to play home games in Oman.
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Mourinho refused to speculate on whether or not he would succeed Van Gaal at Old Trafford having formed a close bond with the Dutchman when they worked together in the 1990s at Barcelona.
"Van Gaal is my friend, I worked with him for a few years. I am always linked with jobs and in the summer I will have a job, but in this moment I can promise you I do not have a contract with any club," he said.
Mourinho said that he would prefer to work in England where his family is settled.
"I am not in position to turn down (jobs). I am in a position to analyse, this is April, everything starts in July, every decision is made between May and the start of June," he said.
"I would prefer (to stay England). I love the country, the football here, my family is very stable and happy."
The former Real Madrid, Porto and Inter Milan boss also said he would like to see Claudio Ranieri, the man he originally replaced at Chelsea in his first spell, lift the Premier League title with Leicester.
"I think his (Ranieri's) career deserves that. He is a good man who I respect. In spite of bad words, he knows I like him very much and I would like him to win.
"Let's go for the simple one -- the one with more points deserves to win.