The Spaniard, who works for Barcelona radio station Moguts pel Barca, indicates the deal is done and will be confirmed soon.
Earlier today Chilean journalist Maks Cardenas claimed the former Barca forward wanted to join City but Arsene Wenger was delaying the deal.
Sanchez has just over 12 months left to run on his current Gunners deal and appears to want to leave.
But this is the biggest claim to be aired regarding Sanchez's future so far.
Romero tweeted: "Alexis Sanchez will be Manchester City player in the coming days."
Last week Wenger insisted Sanchez and fellow contract rebel Mesut Ozil would not be leaving The Emirates this summer.
He said: “They love the club.
"They integrate well the values of our club and they want to be part of it because they love the football we play.
What's hot
"This summer they will stay at the club and hopefully we can extend their contract.
"You cannot weaken the club and weaken the team.
"And you want to strengthen the team unless you find a player of the same calibre unless they want absolutely to leave.
"I believe that at the moment, we are not on that front.
"We are just focused on keeping the team together and seeing how we can strengthen the team."