One of the finest midfielders of his generation, the 43-year-old had no shortage of suitors during his 17-year spell at Anfield from 1998 to 2015.
Chelsea failed with a swoop for the 2005 Champions League winner, while Real Madrid and Inter Milan were also knocked back in their approaches.
And Manchester United icon Neville has now revealed that Sir Alex Ferguson tried to get him to convince Gerrard to swap Merseyside for Old Trafford in 2004.
In what would have been one of the most shocking transfers in history, Gerrard would have become the first player to directly transfer between the two bitter rivals since 1964 when Phil Chisnall joined Liverpool.
But Gerrard refused to entertain the idea, as he is claimed to have expressed fears over the safety of his family if he had swapped clubs.
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Speaking on The Overap's 'Stick to Football' podcast, Neville said: "Stevie told this in his book, where I went into his room with England and asked him to sign for Manchester United.
"I was meeting up with England for the Euros, and he [Ferguson] rang me and said it's ambitious, but his words were, 'Tell him I'll go and fetch him, and I'll walk him back down the East Lancs'.
"I went to see Stevie, and he quite categorically [rejected it] pretty quickly.
"He said he would never get out of Liverpool and his family would never get out of Liverpool."
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Gerrard has been quick in responding to Neville's retelling of the incident, as he took to his Instagram story to issue a six-word statement.
He simply posted: "It was a polite f*** off."
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The Reds cult hero did eventually leave Liverpool - joining MLS side LA Galaxy in 2015 on a free transfer.
He subsequently retired in 2016 following the expiration of his 18-month contract in America.
Only Ian Callaghan and Jamie Carragher havemade more appearances than Gerrard's 710 games for Liverpool.
Meanwhile his 186 strikes place him sixth on the club's all-time goalscorers list.