The Greek international is set to make a decision over his future.
It was reported by Metrosport in Greece that the Greek international striker is a transfer target for Forest.
The report claimed that Forest are keen on signing the player, who is valued at around €1.2 million (£940,000), as they seek to bring in some striking reinforcements.
It was then reported by the Nottingham Post that this deal had been accepted.
In the latest developments in this story it has been reported that Vellios has offers from two clubs – and Greek giants Panathinaikos are also considering a deal.
Contra are reporting that AEK Athens is his other option, whilst Panathinaikos are also interested. His current club Iraklis however are keen on him to move to Forest – to avoid him joining a rival and for the best financial package.
In another update on the matter Prisma report that Vellios has headed on holiday to Crete with friends and no decision on his future is expected until he returns.
Vellios has finally found his feet at Iraklis after struggling since his Everton exit.
The Greek striker impressed at Goodison Park when he did feature but struggled with stints in Belgium and Denmark.
Last summer he headed home to Iraklis. He scored 13 goals in 2015-16 from 32 games and recently secured himself a place in the Greek national team for the first time.
Forest are on the hunt for new striking reinforcements and are now just waiting on Vellios to return an answer to their successful bid.