Lukaku joined Everton on transfer deadline day on a season-long loan from Chelsea.
Lukaku impressed during a spell on loan at West Brom last year.
“I chased him all summer to be honest,” said Allardyce.
“But when it became the final day of the deadline we missed out and Everton managed to secure his position.
“We were more or less told he was going back to West Brom. We tried, but didn’t manage to clinch it.”
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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.