The 23-year-old has found the back of the net 12 times for Chelsea in 30 appearances across all competitions this season, but has fallen down the pecking order at Stamford Bridge.
Since returning from his injury earlier this month, Abraham is yet to feature for Chelsea as manager Thomas Tuchel has chosen not to field him.
West Ham legend Cole believes that Abraham would fit in perfectly at the London Stadium and could form an exciting partnership with Lingard, who has resurrected his career following a loan switch from Manchester United earlier this year.
Cole is impressed by the young striker’s technical ability and physical attributes as he insisted that Abraham would be ideal to lead the front line at West Ham.
“If he was to come to West Ham, I’d welcome him with open arms”, Cole told Bookmakers.co.uk.
“He would be the perfect person to lead that front line.
“We’ve got Michail Antonio there, who is a top player, but Tammy could come in and challenge for that place and that’s what West Ham need, there’s no one to challenge Antonio.
“Tammy would be perfect.
“I’ve always liked a technical big striker and he could be the ideal fit for West Ham because they can play a bit of football this team, and he’d fit straight in, especially if we can keep Lingard.”
Abraham will look to break into Tuchel’s Chelsea side before the end of the season as they chase a top four spot in the Premier League along with Champions League and FA Cup glory.