Sky Sports reports that Foxes head of recruitment Steve Walsh has twice watched Robson-Kanu at Euro2016 and the East Midlands outfit could be ready to lodge an offer.
However, there are believed to be other clubs such as Swansea City, Watford and Celtic keen on Robson-Kanu who scored a stunning goal with a 'Cruyff turn' in Wales' 3-1 victory over Belgium in the Euro quarter-finals on the weekend.
The player admits that his agent has been busy fielding calls regarding his availability in the current transfer window as he and his Dragons teammates continue to surprise all before them in France.
"Yeah he has!" said the Arsenal youth product.
"It's one of those things, it's quite a unique position but as a player my focus is on the next game and we're taking it seriously.
"That will look after itself."
After the win over Belgium, Robson-Kanu insisted that he will not contemplate his club future until after his national team obligations are complete.
"I said before the tournament I would make a decision on my club future after Euro 2016 and that's the way it stands," he said.
"But I am aware of the interest in me now after what has happened here.
"The last couple of summer's clubs from the Premier League have come in for me and the bids were rejected. So I have run my contract down to be in a position to decide where I want to go."
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