United haven't signed a central midfielder since Owen Hargreaves and Anderson arrived in the summer of 2007.
And since it became clear that Hargreaves was never going to recover from the knee injuries that blighted his Old Trafford career, they have looked short in midfield.
Anderson has shown that he's capable from time to time, just not every week. Paul Scholes retired, made a comeback, then retired again while Darren Fletcher is still battling to overcome a stomach condition with no date for his return.
Tom Cleverley is still learning, even though he's an England international and Nick Powell, a 19-year-old, isn't ready yet. Given the circumstances, Moyes could be forgiven for wanting to wrap Michael Carrick in cotton wool.
Who is the best replacement for Patrice Evra at Manchester United?
But alongside Moyes' pursuit of a midfielder is that of Leighton Baines.
The Everton full-back is a fine player, the best left-back in the Premier League last season. There are few full-backs in the world who can boast his energy and delivery, either in open play or from set pieces. He's now even pushing Ashley Cole to start for England.
But as good as Baines is, he'll be 29 in December.
Patrice Evra, United's current left-back, struggled for form two years ago but last season returned to something like his best. The Frenchman is 32 and will need replacing sooner rather than later, but a player approaching 30 himself is hardly a long-term alternative.
Southampton's left-back is only 18 and already has a season of experience in the Premier League. He was impressive on the opening day of the season, bursting into the area in the last minute to win the penalty which earned a 1-0 win over West Brom.
Southampton would fight any bid for Shaw, but they're unlikely to be able to say no forever. United, meanwhile, have a record of trusting young players, you only need to look at their pursuit of David De Gea.
It would have been easy for them to look for an experienced goalkeeper to replace Edwin van der Sar, but they signed De Gea and now they're reaping the benefits.
If De Gea keeps progressing in the same way, United won't need to look for another No. 1 for 15 years. Shaw would represent a similar long-term investment.
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