Lukaku has been in wondrous form for Everton this season and is the Premier League's top scorer along with Tottenham talisman Harry Kane with 19 goals. The 23-year-old is also close to signing a new five-year contract worth £140,000-a-week at Goodison Park, despite constant ongoing speculation surrounding his future.
But Collymore thinks Ronald Koeman's men may struggle to fulfil the Belgian international's ambitions in the short-term and believes Tottenham should test the Merseysiders with a move at the end of the season.
"All great players have competition and I know that in 2017, players are more prissy, more demanding and off quicker when someone takes their place," Collymore wrote in his column for Boylesports. "But (Harry) Kane is going nowhere for the next couple of seasons at least and maybe longer if the trophies start to come in.
"So go and break the bank and get someone who is arguably better than Kane, or at least on the same level, and you know who that would be for me? Romelu Lukaku.
"Seventh is the summit of Everton's ambitions for the next two seasons. Don't get me wrong Evertonians, I'm not trying to sell your player, but look down the line two years, unless the Toffees win trophies which, with the competition above them looks unlikely.
"Everton could command big money for Lukaku and if we are all being honest, like Kane at Tottenham, unless either win trophies in the next two years with their current clubs, both will be off!"
Everton resisted summer interest in Lukaku from Chelsea, who balked at the Toffees' £75m valuation for their former starlet, but Collymore thinks Antonio Conte's side would be one of a host of Premier League clubs that would love to lure the former Anderlecht prodigy away from Goodison Park if an opportunity arose at the end of the current campaign.
"Chelsea, City, United and Arsenal all arguably would be interested if Rom became available, plus many clubs from abroad would be interested but I can't stress enough that modern players want to live in London," added Collymore.
"He's been in the capital once with Chelsea and the way Tottenham play, the creativity behind a solo striker or pairing (flexibility that Tottenham need over several tournaments) would fit him hand in glove."