The ex-Spurs manager and midfielder also claims the north London derby means a lot less to the players now than it used to...
Sherwood was a Gunners fan in his youth and admits he almost joined the club in the summer of 1996, when Bruce Rioch was manager.
The move never materiliased, however, and the midfielder joined Spurs three years later, also becoming their manager for a brief period last season.
Instead, Arsenal signed Patrick Vieira - and that didn't work out too badly for the Gunners...
"I was days away from becoming an Arsenal player in the summer of 1996," Sherwood wrote in his column for the Independent.
"When Bruce Rioch called me at home on an August night, I expected him to tell me what time to get to London Colney for my medical. Instead he told me he’d been sacked and the deal was off. They ended up signing some lad called Patrick Vieira.
"Three years later I joined Tottenham Hotspur and went back to my north London roots."
Meanwhile, the 45-year-old has also criticised the mindset of modern players, suggesting the north London derby is not as important to them as in the days when himself and Vieira took to the field.
"Does it mean as much to the players now? I think the culture has changed," Sherwood mused.
"You see players from opposing sides chatting or embracing in the tunnel before the game. It would never have happened when I was a player. On that day, we loathed the Arsenal players as much as our fans loathed theirs."