Ukranian outlet Sport Arena also reported that the Bhoys are close to completing a move to sign the Karpaty winger in a deal around £2million.
Brendan Rodgers has looked for young and promising players to bolster his squad rather than experienced stars in January, and Shved has been linked heavily with a move to Parkhead.
Celtic have signed three young players – Oliver Burke (21), Timothy Weah (18) and Issouf Bayo (22) – this month already and it looks like Shved is on his way to join the Scottish champions.
The report claims that Karpaty have left him out of their winter training camp to complete the deal.
The club vice-president has confirmed that the player is in advanced talks for a move.
Karpaty Lviv’s vice-president Oleg Smaliichuk said: “Maryan did not travel with the squad to Turkey because we are negotiating his transfer with another club.
“The offer meets our valuation and, above all, if the player himself is satisfied with the offer, then he will leave us. I must stress that these players are not being sold because we are in some sort of great New Year’s sale.”
Shved has been in terrific form this season for the Ukrainian club, scoring eight goals and creating three more in 17 league games for them.
Ukranian club Dynamo Kiev have also shown an interest in signing him but it seems he is heading towards Celtic Park instead in January.