A new name has been linked to Liverpool this week, although one which will be familiar to Manchester United supporters.
It was The Telegraph who claimed in early 2012 that Manchester United had agreed a deal for Gaitan, with Federico Macheda and Fabio da Silva set to go in the other direction and a £20 million fee decided upon.
For one reason or another, Gaitan remained at Benfica, and still does - and while he lacks the sort of goalscoring figures from a midfielder to make fans who have never seen him play sit up and take notice, he remains a special player capable of conjuring up a moment of magic capable of winning any match.
Here are two spectacular examples, one a flicked volley so unique we simply can't begin to try to describe it, other than it's a goal of the like that we don't see being replicated any time soon.
The second was a set piece netted last week in the Europa League, one which rather than being a chipped 'Panenka-style' penalty, was a free-kick delicately lifted over the wall.
Neither are goals which you expect the likes of Victor Moses or Ashley Young to think of, let alone executing to perfect.
So with Liverpool linked with his signature, should they succeed and get the best out of Gaitan, every goal, assist, or moment of magic would resonate with Manchester United fans - that they should have had the player already.
And this would be one David Moyes could not cop the blame for. As it was Sir Alex Ferguson who had the opportunity to sign Gaitan, but elected not to do so.
In fact it is symptomatic of a lot of the glaring gaps left for David Moyes to try to cope with at United, while the boss has not helped himself in several instances, namely getting rid of the existing coaching infrastructure, Ferguson's reluctance to add enough quality to the first team squad at Old Trafford left his successor what many consider a bit of a poisoned chalice as much as an opportunity of a lifetime.
By signing Gaitan, Liverpool would be telling United: 'Look you had your chance to push on, and you blew it. We're here in the Champions League places now, and won't be waiting around for it all to fall apart. We are going to get bigger and better, catch us if you can'.
image: © Crystian Cruz