Despite their absence, the Blue Machine came from behind to beat San Luis 2-1 at home on Saturday with both goals from their Argentine midfielder Christian "Chaco" Gimenez to take their tally to four points from two matches.
Some clubs had been unaware they would be affected by a Mexican government rule introduced in November under which foreigners coming into the country to work need to arrive with their permit in hand rather than making their application once in Mexico.
Colombia striker Gutierrez and former Boca Juniors and Banfield midfielder Bertolo were going to travel to neighbouring Guatemala to apply for their work permits at their respective countries' consulates on Monday, the daily El Universal said.
"This lack of communication (between the league and teams) is worrying. At the end of the day, those affected are me (and) my team," Cruz Azul coach Memo Vazquez said.
Gutierrez, who got a name as a trouble-maker at Racing Club in Argentina last season after pointing a paintball gun at angry team mates in the locker room following a sending-off, was signed from Colombia's Atletico Junior.
Bertolo has joined Cruz Azul from Italian Serie A side Palermo.
Queretaro could be fined for fielding Colombians Wilberto Cosme and Omar Vasquez and Peruvian Juan Carlos Marino in their opening 2-2 draw with Leon. The trio were absent from Saturday's 2-1 home win over Pumas UNAM.
"It's a visa matter. We're not going to lose the point because it's not a footballing question, but of immigration," Queretaro vice-president Markus Lopez was quoted as saying by El Universal.
Lopez said he had been reassured by Liga MX president Decio de Maria, who told El Universal: "Yes, they got a sporting advantage...but we're not going after them."
Argentine striker Mauro Matos arrived in Mexico City last week to sign for San Luis on loan from All Boys of Buenos Aires only to be deported because he did not have a work permit.
Matos, one of some 100 foreign players in the Mexican league, obtained the permit this week.
"I was really keen to come here and never lost my desire to come (to Mexico). It was a nasty moment but it's history now," Matos said.
After two rounds of the Clausura, the second of two championships in the Mexican season, America and title holders Tijuana are on a maximum six points with four clubs, including Cruz Azul and Queretaro, on four.
Tigres UANL, with three points, can go joint top if they win at Atlante on Sunday.
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- Cruz Azul