The Chilean international's contract at the Emirates runs down after the end of the next season and he has not agreed to sign a new deal. He scored 24 goals and registered 10 assists for the Gunners this season and his impressive form has seen him attract interest from the Premier League winners, Manchester City and Bayern Munich.
Aguero, on the other hand, has scored 31 goals across all competitions for Pep Guardiola's side. This includes 20 goals in the league but the arrival of Gabriel Jesus has seen him play second fiddle to the Brazilian.
Cole, who is now plying his trade with American club Tampa Bay Rowdies, believes the addition of Sanchez and Aguero or one of them to the Chelsea squad will make them the firm favourites to win the title next season.
"I'd go, 'Go get me Aguero or Sanchez or both, and I want no one else,' and I can guarantee you they'll win the league next year," Cole told Goal.com.
"The thing is everything is in place. Everyone keeps talking to me about, 'Oh, they need to replace Moses or Alonso'. They don't, they've been brilliant. You don't need to replace them.
"There's enough young players as well in the academy that can come. They just need an extra bit. What [Sir Alex Ferguson] did well over the years is reignite with one or two big players."
"Realistically, you could build to the future and spend a fortune and try and go and get [Harry] Kane and all from Tottenham, but I think that's not going to happen, they're not going to move them.
"You think Aguero and Sanchez there's maybe little bit of instability at their clubs so I'd be moving heaven and earth to get both of them, or one of them."
Antonio Conte helped the west London club win the title in his debut season and has an opportunity to help them win the FA Cup. Chelsea will face cross town rivals Arsenal in the final at Wembley on 27 May.