The 25-year-old goalkeeper is on loan at Getafe from Arsenal at the moment, but it has been reported that the Spanish club could let him leave if they manage to keep hold of Vicente Guaita, who is claimed to be of interest to Premier League club Crystal Palace.
Martinez is 25 years of age and has made only a handful of first-team appearances in his professional career so far.
However, there is no doubt that former Argentina Under-20 international is hugely talented, with Arsenal manager Arsene Wenger describing him as a world-class goalkeeper to The Metro in 2017.
Celtic, though, will have no one but themselves to blame if they miss out on Martinez to Leeds in the Championship in England.
True, Craig Gordon’s injury is only recent, but the Scotland international has not been in great form for a while now and has made mistakes from time to time for the past two or so seasons.
Celtic manager Brendan Rodgers should have at least looked at the possibility of signing Martinez from Arsenal back in the summer of 2017 before he went on loan to Getafe, or at the start of the January transfer window.
With Argentina AS claiming that Leeds are set to sign Martinez, Celtic could miss out on a talented and promising goalkeeper who would have walked into the Bhoys’ first team and would have been an upgrade on the goalkeepers they have.