The Ibrox side have been strongly linked with the Bologna winger with his future at the Serie A side up in the air.
Giovanni van Bronckhorst is keen to add more width to his options in attack.
The 22-year-old moved to Bologna for €6million in 2019 after a stunning season in the Danish top-flight with Nordsjaelland when he scored 26 goals in all competitions.
However, he hasn’t been able to replicate that form, or that with the Danish national team where he has six goals in 15 games, in Italy.
He has been in and out the team and, at times, playing out of position.
Rangers could face competition for his signature. FC Copenhagen, Torino and Hertha Berlin have all been linked.
Aberdeen’s Calvin Ramsay could play a role in the deal with Bologna keen to sign the full-back this window. Skov Olsen has featured in the right wing-back role recently and it could be the case of one in, one out at the Italians.
A possible move to Ibrox for the winger has been given the seal of approval by Rangers legend Brian Laudrup who has admitted his excitement at the prospect of his countryman making the switch.
"If you are looking for a hug the line player, a real creative force, then Skov Olsen ticks the boxes," he said. “I think he would be wonderful to watch in a system like Giovanni van Bronckhorst's.”