Reports: Cabanas dared attacker to pull trigger
Cabanas, a prolific goal-scorer who was expected to lead the Paraguay attack at this year's World Cup, was shot in the bathroom of a Mexico City bar in the early hours of Monday.
He remains in critical condition with a bullet lodged in his brain.
Another man in the bathroom taunted Cabanas over his recent scoring record and held a gun to the footballer's head. Cabanas then dared him to shoot, Reforma newspaper reported, citing a bathroom attendant's statement to police.
Cabanas, 29, plays for Mexican club America and was Paraguay's top scorer in the qualifying competition for this year's World Cup in South Africa, with six goals.
Police are looking for a man they believe regularly visits the bar, popular with Mexican celebrities and VIPS, after spotting him and his bodyguard on security cameras.
Doctors say any attempt right now to remove the bullet would further endanger Cabanas.
"His situation is stable but he is still in critical condition," America spokesman Edwin Victoria told reporters on Thursday.
Cabanas was also top scorer in the 2007 South American Libertadores Cup with 10 goals and again the following year with eight, both while playing for America, Mexico's richest and most powerful club.
He has regularly been among the top scorers in the Mexican championship since moving to the country in 2003, initially with Chiapas until 2006 and then with America.