Vellios is on the books of Iraklis at the moment and has a contract with the Greek club until June 2017, according to Transfermarkt.co.uk.
According to a recent report in The Nottingham Post, Forest are interested in signing the 24-year-old striker this summer.
Vellios, who has played three times for the Greece national team, scored 13 goals for Iraklis during the 2015-16 campaign.
The 24-year-old started his professional club football career at Iraklis and was on the books of Everton from 2011 until 2014.
The Greece international striker failed to make an impact for the Merseyside outfit during his spell at Goodison Park.
Forest fans have taken to Twitter to have their say on the prospect of signing Vellios in the summer transfer window.
Below are some of the best comments:
if true, what is the point in us trying to sign vellios? was awful at everton and scored 11 goals in a btec greek league last season #nffc— jake kervick (@jakekervick) June 13, 2016
Genuinely no friggin idea who authorised the bid for vellios. Maybe matty fryatt has been scouting him in greece for the past year? #nffc— Sam Crawford (@s_redmist) June 9, 2016
Vellios wasn't tremendous in England last time, but he can't be worse than Bader Al Mutawa - remember him? Fawaz's present? #NFFC— Christian Brown (@Chris78901) June 9, 2016
If Football Manager has taught me anything, it's that Vellios would be a decent signing... #nffc— Smash! (@noggin2k1) June 9, 2016
I don't know why we would sign Vellios. He's another Veldwijk, except Veldwijk is better. #nffc— Elephant Juice (@ElephantJuices) June 9, 2016