The 24-year-old winger has scored six times for PSV Eindhoven this season but will be out of contract at the end of the season.
He is unlikely to sign a new deal with the Dutch club and it has started a fierce race amongst the two Glasgow rivals to secure his signature on a Bosman deal next summer.
Both Glasgow clubs are interested in signing him on a free transfer and are pushing to secure an agreement.
Gudmundsson will be free to hold talks with suitors over a pre-contract agreement from next month onwards.
Both Celtic and Rangers have identified him as their major target given his contractual status and are looking to move in for him.
Rangers are currently leading the league table, with Celtic just behind them, with both clubs looking to secure automatic Champions League group stage qualification for next season by winning the title.
Gudmundsson has not made up his mind and there are several other clubs who are interested in him as well.
But there is a battle on in Glasgow to secure a deal to take him to Scotland next summer.