The 26-year-old has been in fine form for Genoa this season, scoring 11 goals and providing three assists in 23 appearances in all competitions.
Gudmundsson has tended to play as a second striker for Genoa this season, but he has showcased his versatility in the past to operate as a wideman and a centre-forward.
The Rossoblu were forced to fend off interest from fellow Serie A club Fiorentina during the January transfer window.
Fiorentina allegedly made at least a couple of offers for Gudmundsson, including one bid believed to be worth €22m (£18.7m).
Genoa ultimately rejected Fiorentina's advances to retain the Iceland international for the remainder of the campaign.
Fiorentina's failed attempt to recruit Gudmundsson in the January window could open the door to two interested Premier League sides.
According to Calciomercato, Tottenham and Newcastle are keeping tabs on the player's progress as they weigh up whether to make a move in the summer.
Genoa are in a strong position when it comes to negotiating a sale, with Gudmundsson under contract until the summer of 2027.
As a result of the forward's lengthy contract, Genoa are only expected to entertain offers that meet their €30m (£25.6m) asking price.
Should Tottenham decide to step up their interest, they will look to utilise their positive relationship with Gudmundsson's current employers.
As for Newcastle, they are seemingly on the lookout for attacking reinforcements, with uncertainty surrounding the long-term future of Callum Wilson at St James' Park. body check tags ::