The 31-year-old's arrival has not yet been confirmed by Fire, but the deal is expected to be announced soon.
Gaitan joined the CSL outfit in February last year from Atletico Madrid and made 28 appearances last season, scoring twice.
The former Benfica man became a favourite among Dalian supporters, but the arrivals of Marek Hamsik from Napoli and Emmanuel Boateng from Levante during the transfer window hastened his departure.
Gaitan started his career at Boca Juniors and has been capped 16 times by Argentina.
He will be expected to form a formidable midfield partnership with Germany great Bastian Schweinsteiger in Chicago when the Major League Soccer season kicks off this weekend.