The former-Stamford Bridge midfielder admitted he harbours ambitions of managing at the highest level, after experiencing success during his short stint on the south coast so far.
And the Ex-Uruguay international doesn't feel his Chelsea past should prevent him from manning one of the other big clubs in London.
"I want to manage at the highest level and would love to manage Chelsea or Arsenal. Why not?" said Poyet.
"Does my Chelsea or Tottenham past mean I cannot be Arsenal manager? Look, I've been at Leeds [as assistant to Dennis Wise] and the relationship between Leeds and Chelsea was not the best.
"If you ask any Leeds fan, my relationship with them was absolutely exceptional.
"I would love to go back to Leeds because they know how much I care for the club and how much I will give the club. Same with Arsenal. The only thing is I need to be ready."
Brighton take on Arsenal in the FA Cup fourth round on Saturday, with Arsene Wenger's side desperate to progress as they look to end their seven-year trophy drought.
The Gunners are all but out of the Premier League title race, and face a tricky Champions League last-16 tie against last year's finalists Bayern Munich.
That leaves the FA Cup as their best chance of silverware this campaign, but Gus Poyet's side have been going well in the Championship this season, and should pose a stern test for the Premier League club. Poyet spent four years at Chelsea, winning an FA Cup and a UEFA Super Cup during his time at Stamford Bridge, establishing himself as something of a fan favourite in west London, before he moved on to White Hart Lane.