Having won La Liga last season, Atletico coach Diego Simeone has been building a squad to challenge again this term, although Diego Costa's sale to Chelsea has heightened the need for attacking reinforcements.
Mario Mandzukic has already been acquired from Bayern Munich, with Antoine Griezmann's arrival from Real Sociedad also set to add a threat.
America president Jose Romano revealed the Spanish side had made an offer for 24-time Mexico international Jimenez, a member of his country's World Cup squad, but will put the decision in the hands of the club's fans.
He said: "We had an Atletico de Madrid offer for Raul Jimenez, but we will not accept or reject it, as we want to gather our fans' opinion regarding this.
"If the offer is good, I guess the player will leave."
Jimenez, who scored 30 goals across the previous two Liga MX campaigns and has four to his name already in 2014-15, has talked up a potential move to the Vicente Calderon, having faced Atletico in pre-season.
He is quoted by Marca as saying: "It is a dream, something I've always wanted. I've been given the opportunity and I want to take it.
"They are the champions of Spain and I want to go on to win a spot."
