The current Brighton & Hove Albion boss spent time with both of Arsenal's London rivals during his playing career in the Premier League.
However, the Uruguayan has revealed that he would not let any disputes between clubs prevent him from fulfilling his ambitions.
"I want to manage at the highest level and would love to manage Chelsea or Arsenal. Why not? 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," he told the London Evening Standard.
"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."
Poyet's Brighton will take on Arsenal in the FA Cup this weekend.