According to The Athletic's Adam Leventhal, Leicester and Everton have both prepared bids to sign the 25-year-old in the summer.
The Brentford striker has had an outstanding campaign, scoring 30 goals and providing ten assists in 44 Championship appearances this season, as Brentford qualified for the play-off spots.
Apart from Leicester and Everton, Spurs have reportedly also shown significant interest in him, seeing him as possible back-up for Harry Kane.
Everton need more options up front, especially due to their struggles when either Dominic Calvert-Lewin or Richarlison have been injured, with Josh King, who arrived in January, struggling to hit the mark for the Toffees.
The Toffees are reportedly interested in Manchester City's Sergio Aguero, who could be set to land the 32-year-old as a free agent, however he is keen on playing Champions League football next season, and they is only a slight chance of them playing in Europe's top competition next season.
On the other hand, Leicester need a long-term replacement for Jamie Vardy, even though Kelechi Iheanacho has been on top form over the last few months, and they are one of the favourites to land the signing of Toney this summer.
Spurs seems like the unlikeliest option, with chances at regular football being very limited due to him competing with Kane, but if the Spurs captain opts to leave the club this summer, then Toney could be interested in joining the London-based club.