The Hoops were represented at Benfica's game against Porto nine days ago, and again at their match against Maritimo on Sunday.
Although Djuricic did not get off the subs' bench on either occasion, he is understood to be the man in their sights.
The 21-year-old only moved to Portugal from Heerenveen last summer in a £5.8million deal, but he has struggled to break into the side in Lisbon.
Having signed him on a five-year contract, if Benfica can be persuaded to sell then they will want to recoup their outlay - with a little on top.
Neil Lennon has already said Celtic still have the funds to buy a £6m player - and Djuricic could be the man. He is already very well known to a handful of Hoops players as he scored both goals when Serbia defeated Scotland 2-0 in their World Cup qualifier in Novi Sad 10 months ago.
Djuricic had by then caught the eye of Sir Alex Ferguson, who invited him to Old Trafford for a trial. But, work permit issues prevented United taking the chase any further and he remained with Heerenveen until agreeing to move to Benfica.
Djuricic has a history of going where he believes he can progress his career, leaving Red Star Belgrade when only 15 to join Olympiacos in Greece.
But it didn't work out as he would have hoped in Greece, and he returned to Red Star where he quickly established himself as one of Serbia's rising stars. Heerenveen came in for him in 2010, and he jumped at the chance to move to the Eredivisie.
Celtic watched the Dutch club regularly as they tried to sign Djuricic's team-mate, striker Alfred Finnbogason, so the Serb has been on their radar for a long time.
Djuricic has already earned 15 caps for Serbia, and fits the Celtic signing template of a young player whose value will rise as his career develops.
Lennon concedes goalscorers and creative midfielders - the positions he has identified as needing an injection of quality - are the toughest to find as they come at a premium price.
Lennon said: "Yes, that's true, absolutely. You are hoping you can always find another Gary Hooper for £1.5million, if you can. But it proves more and more difficult because a lot of clubs like to stockpile strikers."
Anthony Stokes has been the Hoops' first-choice striker for most games in the first half of the season, but, the red card he picked up against Motherwell means he is suspended for Sunday's match against Hibs at Easter Raod.
That has increased the need to step up the hunt for the proven goalscorer Lennon wants.
"We have got Teemu Pukki and Amido Balde," said Lennon as he assessed his existing options for the weekend. Hopefully, Georgios Samaras will be fit, so I have plenty of options there. And I might have one in by then, you never know."
Lennon is also considering sending more players out on loan to accelerate their development. Tom Rogic today begins four months with Melbourne Victory, who won the three-way fight to take him back to the A-League.
The Australian FA have confirmed the three-match suspension he incurred after being sent off in his final game for Central Coast Mariners before he moved to Celtic last January has now been served.
That leaves the way open for the 21-year-old to make his debut for Victory - managed by former Rangers midfielder Kevin Muscat - against Sydney FC on Sunday.