The 25-year-old joined Brentford from Peterborough last summer and has been a revelation in the Championship, scoring 28 times in 38 appearances.
Toney was in demand last year and there was talk of Celtic also wanting to sign him before he moved to Brentford.
And it has been claimed that former Celtic boss Neil Lennon was desperate to land him and the striker even agreed terms on a contract with the Bhoys during a secret visit to Parkhead.
But Lennon was ultimately disappointed to miss out on the forward after Celtic failed to put in a good enough bid.
The Scottish giants failed to put in an offer to match the bids Peterborough received for Toney last summer.
And ultimately Celtic were beaten by Brentford to the signature of Toney, while the Bhoys signed Albian Ajeti from West Ham.
Lennon ultimately left the club in February after failing to help Celtic win their tenth league title in a row.
Toney is likely to attract interest from the Premier League this summer after a terrific season in the Championship.