Beckham made his Football League debut as a teenager on loan at Deepdale and has a personal fortune estimated at around £100m.
He has expressed interest in investing in a club when he finally hangs up his boots and Shaw would welcome his arrival at Preston.
"We all remember David and I'm sure he remembers the time he spent here - even though it was only a month," Shaw said.
"If he has still got our phone number then we'd be delighted to hear from him. We have always made it clear that we would be prepared to talk to anyone who has a genuine interest in this club and would like to invest.
"I know David has spoken well of Preston North End over the years. And if he is looking for a club to get involved in, then what better club than the one he made his league debut for?" Tweet

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David, use your clout and put a team of investors together and get us out of debt. Give the Glazers a nice profit and they will go away. When I say investors I mean people with actual cash to invest and not investors with the ability to go out and obtain a financing package which involves every pound spent being analyzed to death and the average punter getting bent over with nothing but axle grease to alleviate the pain.
We seem to be able to end up with players we want but every deal is a nightmare. This is Manchester United, the biggest club in the world. We should be debt free with owners that are fans as well as owners and stay right in the background letting Fergie and Gill get on with it. Anyone who thinks they have a free reign is not in the real world. Personally I don't want to know about deferred interest payments and don't feel it should even come out in print. By the way if Becks is worth 100 million then it means he has no more than 10 to 20 million to invest. Chickenfeed to the big boys.
Go on Becks they've got a chance of becoming bigger than Man Ure now so go for it!
Heres a better idea David...go back to your roots and discover your passion for the game or did you ever have any? And i agree, you don't have what it takes to become a manager
David Beckham mix it with rough, tough northerners? My bum!
She (who must be obeyed) would have the team playing in Armani knickers and blowing the opposition away with the stench of their Hugo Boss aftershave.
Want a team to buy, Becks? Try some southern fairies and stay away from the NorthWest. We need you as much as a hole in the a--e, sorry, head.
David Beckham is the only becon of English football recognised around the world. Or is there some other player who is on the tips of every ones tonges in every country on the fase of the earth.He was never the best player in the world.but at least he was in the world of the best players. Flying the union jack for Queen and country.Like it or not he,s still one of the biggist sports personalitys in the world. You beckham knockers make me sick. Or maybe you are not realy british maybe thats your problem.If so go back where you came from, or keep you mouth shut. if you have nothing positive to say don,t say any thing at all.If he blasts ENGLAND into the world cup i just wonder what you lott will have to say then.There are lotts of people around the world.slagging britain off every chanse thay get with out clowns like you lott HELPING them do it. Come on who has done as much as Beckham for our national image, world wide...... Time up the answer is the beatles and Lady Diana.O.K.He,s not a dreamer he,s a do,er you sour grapes people got it.
"Come on who has done as much as Beckham for our national image, world wide.....
Winston Churchill, Brunel, Charles Darwin, William Shakespeare, Sir Isaac Newton, Nelson.....