Speculation suggests that Gazza wants to move to a club near London to be closer to his children. The ex-England star is currently looking for a club after being released by Everton.
According to Paul Williams a highly reliable source informed him about the possible deal.
Mr Williams told Reading-Mad.co.uk: "My source of information claims he was with Alan Pardew on two occasions when he received phone calls about Paul Gascoigne.
"The initial reported phone call came from Gazza's agent, Ian Elliott, who offered his clients services for £30,000 per week. This offer was allegedly turned down.
"According to my source the second phone call came from Gascoigne himself who was reportedly willing to accept only £3,000 per week to sign for the Royals.
"It is claimed that Gazza is looking to play for a club near London to be near his kids. He was apparently very impressed by the turn out for Phil Parkinson's testimonial and the reception the fans gave him.
"Pards has reportedly since spoken to John Madejski about the possibility of bringing Paul to the club, citing the added revenue that would be generated through press coverages, shirt sales and attendances as a reason to bring one of England's most loved footballers to the club.
"It was allegedly agreed that Gascoigne would come to the club on Thursday for a medical and to negotiate personal terms - with a view to signing him in time for Saturday's game against Coventry."
Gazza has been written off many times in the past - according to Tony Scholes - editor of Burnley Mad - the 35-year-old is not up to the task of First Division football any more.
Tony Scholes said: "Gascoigne spent the final few months of last season with us but to be honest he isn't really up to the task of First Division football any more.
"He can still pass a ball but he can't go past a player - at times he looked pretty embarassing."