Gerrard was spotted in the Gulf nation recently amid speculation that he could become a new manager in the Saudi Pro League.
Al Ettifaq were heavily linked with the Reds legend, but he revealed that he was not keen on the role when speaking as a pundit on Channel 4's England coverage this week.
Gerrard said on Monday: "A lot has been said in the media, a lot of it is not true.
"I was invited over there to look at a potential offer, which I did.
"I have been analysing that for the last few days but where we stand right now, I won't be taking that offer."
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Speaking on the White and Jordan show, talkSPORT pundit Murphy admitted he was bamboozled by the decision to stay away from the Middle East.
The ex-Liverpool midfielder remarked: "I was a tad surprised, if I am honest.
"I thought while he was over there, the lucrative aspect of it and the way they would have made him feel welcome, I thought he might be reeled in.
"But he has shown some courage and substance there. The one thing I know about Stevie is, he loves football.
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"He loves a challenge and he loves trying to prove people wrong.
"That journey he did amazingly well as a footballer and as a manager now, he has taken some steps forward and gone backwards.
"He is going to have to take a challenge that maybe he did not anticipate he was going to have to, when he started flying at Rangers.
"And maybe something is in the pipeline that we didn't know last week when we were talking about it and he will challenge himself to do that."
Bookies currently hold Gerrard as the shock favourite to take over at Sheffield Wednesday following the abrupt dismissal of Darren Moore.
Despite leading the Owls back to the Championship, Moore was allowed to leave this week.
But Gerrard would face stiff competition with Carlos Carvahal, Nathan Jones and Bruno Lage all linked as well.
The 43-year-old last managed at Aston Villa, where he was sacked in October after 11 months in the job following a run of two wins in 12.