The Parkhead side are on the lookout for signings, with manager Ronny Deila having so far only secured the services of goalkeeper Craig Gordon.
Aquino's club, Villarreal, want to send out the 24-year-old on loan as they have too many non-EU players in their Primera Division squad for the season.
"Javier has three proposals in Europe - not just Glasgow Celtic," said his agent, Mario Ordiales. "I will go to Europe and confirm the deal this week. There are still a number of conditions to be sorted out - for example what percentage of his wages are still paid by Villarreal.
"The issue is between the clubs, not us. Javier still has two years left of his contract in Spain and he will see them out, no question. He played over 30 games last season in La Liga with Villarreal and they still see him as part of their future."
Aquino was a late replacement for Mexico's World Cup squad and played just 29 minutes in Brazil, as a second-half substitute in their second-round defeat by the Netherlands.
Celtic's 19-year-old striker Denny Johnstone, meanwhile, is due to join Birmingham City after being recommended by former Parkhead stalwart Alan Thompson and impressing on trial. The Scotland under-19 cap had seemed likely to move to Dundee United this summer, but the Tannadice club dropped their interest because they would have had to pay a transfer fee, which would be set by a tribunal.
Birmingham appointed Thompson - who was sacked by Celtic two years ago - as their senior professional development coach in the summer.
And, after recommending Johnstone to manager Lee Clark, the striker - who is out of contract at Parkhead and keen to start a new career down south - is lined up to sign for the Championship club after playing in a closed-door trial match at the weekend.
Johnstone was a prolific scorer for Celtic's youth teams and led the line for Ricky Sbragia's young Scots in the Euro Elite tournament in England in May.