The 25-year-old joined the Championship outfit from Peterborough United after bagging 40 League One goals in 76 games in two seasons.
Toney has since hit the ground running in the English second-tier, scoring 29 goals in 40 appearances for the London outfit as they strive to win promotion to the top flight.
He could have been scoring those goals for Celtic, but the Scottish Premiership giants were not particularly keen on him despite showing him around their training centre.
“I was actually very close – I went up there and spoke to everybody,” Toney told talkSPORT (via The Scottish Sun)
“I was actually at the training ground and looking around and all that, so it got to those stages.
“But I just don’t think they were too keen on signing me. I guess it’s their miss now.”
Celtic will the campaign without a trophy, having been beaten to the Scottish Premiership title by Rangers and dumped out of the Scottish Cup by their bitter rivals.
Things might have been different with a striker like Toney leading their line, and the Hoops will surely rue such a big miss.
He is hoping to be playing in the Premier League next season, which will most likely happen with or without Brentford.
Celtic will be looking to make quality additions to their squad this summer to challenge Rangers next term, and they are likely to need a new striker, with Odsonne Edouard expected to leave.