The Daily Express claimed West Ham and Leicester City are set to table offers for the £15m-rated Manchester City winger, who has been on loan at Scottish champions Celtic for the past two and a half years.
It is believed that Celtic are also keen on keeping the former Fulham star, who is renowned for his quick feet and ability to open up an opponents defence, boasting vision and an eye for goal of his own.
A West Ham fan asked McAvennie - who is regarded as somewhat of an icon at Celtic, too - what he thought about Roberts and whether the England youth international would fit in at the London Stadium.
In 78 league and cup appearances for Celtic, Roberts was involved in 44 goals for Brendan Rodgers' side as he found the back of the net 18 times as well as laying on 26 assists.
This season, Roberts suffered a long-term hamstring injury that limited the fleet-footed star to just 18 appearances, but has admitted that he is keen on a move to the Premier League.
He has two years remaining on his contract at The Etihad, and any move for Roberts is only likely to be made after Pep Guardiola makes a decision on whether the winger is required at City.