Reports have suggested United are trying to sign 18-year-old Southampton defender Shaw, who has been included in England boss Roy Hodgson's squad for this summer's World Cup.
The left-back already has over 50 Barclays Premier League starts and a senior international cap to his name.
And when asked about the prospect of Shaw joining United, Owen, who made such a memorable impact at the 1998 World Cup as an 18-year-old, told Press Association Sport: "I think it's always good to keep progressing up the ladder and to play at the highest standard.
"And once you have had the experience that Luke Shaw has had in the Premier League, I think you are certainly ready for that challenge now.
"Having had the first-team experience he has, and now going to a World Cup, I'd say he is more than ready to join a really big club - if Southampton let him go."
Should the move to United go through this summer, Shaw will be joining at an interesting time for the club.
The Red Devils are set to undergo considerable change as they look to bounce back from a disappointing 2013/14 season following the retirement of boss Sir Alex Ferguson, with a permanent replacement - Louis van Gaal, it seems - for Ferguson's successor David Moyes coming in and the squad being overhauled
Owen feels the Shaw transfer would be a good one for all parties concerned.
"United have obviously had a poor campaign by their standards and we talk about rebuilding, but it has only been one season - there is still an awful lot of quality there," the 34-year-old said.
"They are a huge club with a huge stadium, and I presume they are going to get a huge manager as well.
"I wouldn't have thought they will be coming seventh again next season, put it that way - I think they will be right back in the mix.
"But they are going to have to buy quality players like Luke Shaw, and particularly in defence, because they have lost Nemanja Vidic and Rio Ferdinand, and there is talk about Patrice Evra as well.
"They are going to be hard to replace, but someone like Luke Shaw would go a long way towards that.
"So the only losers would be Southampton - but then again, I'm pretty sure there will be a huge fee involved!"
Shaw is part of a 23-man England World Cup squad that has plenty more youth in it, with the likes of Ross Barkley and Raheem Sterling also included.
While approving of Hodgson's selection and pleased it features several younger players, Owen has also been keen to stress he believes those chosen have been on merit, regardless of their age.
And he is feeling positive about what the group can achieve at the tournament in Brazil.
He said: "I think a lot of the players we will be pinning our hopes on are youngsters - and that is maybe just a coincidence.
"They have all come off a great season for their clubs, are full of confidence, and I'm hoping one or two of them will star in this tournament.
"I think England are going to surprise a few - I think we could do well."
The future of the national team has been very much on the agenda recently after Football Association chairman Greg Dyke unveiled a set of proposals aimed at boosting the number of English players at the top of club football.
Owen was speaking at St George's Park, where he was promoting the FA's 'Reds v Blues' initiative, designed to encourage people of all ages and abilities to play the game.
And the former Liverpool and Newacastle forward feels the key issue in terms of the England debate is ensuring there is decent coaching at grass-roots level.
"In the initial stages it is just about enjoyment for youngsters - just getting out and about is key," Owen said.
"Then, later on, into your teens, it really is important to get good coaching, better coaching, and have a pathway through to a first team."
The Reds v Blues weekend of football celebrations starts on June 6 and will see people representing a red or blue team, playing the game in whatever form they wish, ranging from kickabouts in gardens to organised five-a-side and 11-a-side matches.
Scores from all the games that take place will be combined to create an overall final score at the end.
Source : PA
Source: PA