But Crystal Palace seem destined for relegation from the Premiership and while Gascoigne has a nationwide appeal the attraction is unlikely to be mutual. While even the most humble of the First Division theatres may be better than some he has trod in Scotland, the thought of his undoubted if flickering talent being cast into the Nationwide hurly-burly is not an edifying one. Paul Merson may be starring in football's repertory but Georgi Kinkladze has been restricted to cameo roles, thus the apparent loan deal rather than a full, permanent transfer.
Gascoigne must be feeling very vulnerable at present. Footballers are never at their best when injured - he has a hamstring problem - and the discovery that he is not wanted by his club will hardly help. For all his ebullience, Gascoigne's confidence can be fragile and it will have come as a shock to discover that Rangers, though struggling to retain the Premiership title, are prepared to let him go before the season's end.
It would appear this decision has been taken as much by the board and the future manager, Dick Advocaat, as by the current one, Walter Smith. Advocaat clearly does not want Gascoigne and the board thus feel the prospect of a deal for a 30-year-old with a history of injury and unpredictable behaviour, is too good to turn down.
They may not be the only ones to feel Gascoigne would be over-priced. His wages will not be cheap, nor the insurance premiums on his fitness. Any fee will be dead money - there is no real prospect of being able to sell him on in a few years' time.
It is possible to see the attraction for Palace. His acquisition would certainly raise the profile of the club - and the apparently headline- loving Mark Goldberg - and it should make the team better. Whether the move is good for Gascoigne is another matter. He needs games to make the World Cup (poor form, injury and suspension have reduced him to completing just four of Rangers' last 16 games), but playing for a poor Palace side will not do him much good this season. It also brings the problems of a London lifestyle.
Palace's chances of landing Gascoigne permanently surely rest on whether they can also attract Terry Venables. The pair have a natural rapport, even if Glenn Hoddle has hinted, none too subtly, that Venables "indulgence" of his occasionally wayward star did Gascoigne no favours.
Derby, Middlesbrough and Newcastle United have also been mentioned. The romantic choice is Newcastle - especially as Gascoigne would be eligible for the FA Cup. Gascoigne may seem an unlikely addition to Kenny Dalglish's dull Roundheads, but the Newcastle manager did try to sign Gascoigne for Liverpool from Newcastle in 1988. Then the problem was money, Liverpool could not afford the pounds 2m fee and, although Gascoigne wanted to go to Anfield, Dalglish said he would have to wait a year. Gascoigne went to Spurs instead.
That was a decade ago, though, and Gascoigne's inability to avoid trouble was not then obvious. Playing for either Newcastle or Middlesbrough would bring him back to the North-east which might ease his peace of mind or, more likely, see him involved in one scrape after another - especially if he chose Boro in preference to Newcastle. If he did go to Middlesbrough he would be building up to the World Cup with First Division football (and no guarantee of promotion), but could play in the Coca-Cola Cup final.
Derby, under the guidance of Jim Smith, are an interesting prospect. Smith may have the personality to bring the best from Gascoigne, who could rise to the challenge of turning an attractive and promising polyglot side into real challengers.
Hoddle will obviously be interested in Gascoigne's decision. Hoddle has repeatedly stressed his faith in Gascoigne but if he is not playing, and playing well, it will be hard to pick him for the World Cup. As it is, his injury makes him a doubtful starter for the friendly in Switzerland on 25 March, leaving just three international matches until the finals.
Any move must be soon - the transfer deadline is 26 March.