The England captain has been heavily linked with an exit this summer, and has not turned up for training this week as he seemingly looks to push through a move to reigning Premier League champions Manchester City.
But despite the fact that Bamford is perfectly content at Elland Road, and even though the Whites have no intention of selling their prized asset, Ashton has still included his name on a shortlist of potential Kane replacements.
Speaking to talkSPORT, he said: “Nuno’s probably thinking, ‘Hang on, I need to know!’.
"Is he going to have Harry Kane for the season? If he’s not, who is he going look at? He’ll have his own ideas.
"Maybe Tottenham fans are wondering how they would replace Harry Kane – you don’t. You don’t just replace a player like Harry Kane, unless you’re going to go and try and spend the same again.
"Nuno might want something different. If you look at who he had at Wolves, Raul Jimenez is the kind of player he clearly he likes, someone to have that role as a centre forward. They’re hard to find, there’s not many around in the Premier League.
"You look at Bamford, who is of that ilk, who can lead the line, work incredibly hard, link the play.
"Jimenez is another if he shows his fitness.
"There will be options there.”
We’ve gathered the best of today’s Premier League speculation below...
1. Villa join McNeil race
Aston Villa could be set to join Everton in the race to sign Burnley star Dwight McNeil, as Jack Grealish edges closer to joining Manchester City. McNeil is likely to command a significant transfer fee, after another impressive Premier League campaign last season. (Liverpool Echo) (Photo by Lewis Storey/Getty Images) Photo: Lewis Storey
2. Albion ready Cucurella swoop
Reports from Spain suggest that Brighton are ready to activate the £15m release clause of Getafe midfielder Marc Cucurella, as they look to get a deal over the line as soon as possible. He made his debut for Spain's senior side back in June. (Sport Witness) (Photo by Clive Brunskill/Getty Images) Photo: Clive Brunskill
3. Battle on for Daniliuc
West Ham United and Southampton have been tipped to go head to head in the race to sign OGC Nice defender Flavius Daniliuc. The Real Madrid youth academy product is currently the captain of Austria's U21 side. (Daily Mail) (Photo by DAMIEN MEYER/AFP via Getty Images) Photo: DAMIEN MEYER
4. Toon eye Skipp
Newcastle United are keen on signing Tottenham midfielder Oliver Skipp, with a move for Arsenal’s Joe Willock appearing increasingly unlikely. (Daily Mail) (Photo by Shaun Botterill/Getty Images) Photo: Shaun Botterill
5. Magpies have not enquired about Ramsey
Newcastle United have not enquired about a potential move for Juventus midfielder Aaron Ramsey, despite reports to the contrary. (Daily Mail) (Photo by Marco Luzzani/Getty Images) Photo: Marco Luzzani
6. Tau bid in pipeline
10-time CAF Champions League winners Al Ahly have prepared an offer to sign South Africa’s Percy Tau from Brighton. (Soccer Laduma) (Photo by Mike Hewitt/Getty Images) Photo: Mike Hewitt