The former Blues star believes a Mexico international striker starring for Wolves deserves to be attracting more interest than he is at present
The Mexico international has starred across 18 months in the Premier League, recording 37 goals in 81 appearances.
At 28 years of age, he should be in his prime and has hinted that he could be tempted to leave Molineux for another step up the ladder.
Frank Lampard wants more firepower at Stamford Bridge while cover for injured stars such as Marcus Rashford and Harry Kane is required at Old Trafford and the Tottenham Hotspur Stadium.
Former Blues star Cole feels Jimenez could be the answer for all of those clubs, telling BT Sport: “Wolves fans won’t thank me for saying it but if I’m Chelsea, Tottenham and Manchester United and you’ve got a chequebook ready to go, he’s the first name.
“If you want someone to make an instant impact on your team, you want someone to tick boxes, who knows the league, knows the flow of English football.
“It’s all well and good being part of a project but when Manchester United, Chelsea and Tottenham come for you, it may turn your head.
“For me, he could quite easily play for any one of those teams because he’s got so much ability. He’s one of my favourite players to watch.”
Ex-Spurs frontman Peter Crouch also believes that Jimenez would be a shrewd addition for Jose Mourinho in north London.
He said: “If I’m one of those big teams I’d be coming in for someone like that.
“He’s an all-round centre-forward. He’s scoring goals, he’s making goals, his link-up play is good, he’s good in the air
Article continues below
“I’m surprised he hasn’t been linked with some big, big moves because he’s been doing this for a couple of years now.”
Jimenez was back among the goals in his most recent outing for Wolves, as he briefly restored parity for Nuno’s side in a Premier League meeting with table-topping Liverpool.
His efforts ultimately counted for nothing, as the Reds ran out 2-1 winners at Molineux, but his stock continues to rise and a window of opportunity remains open to potential suitors until the end of January.