Manchester United manager Louis van Gaal has refused to rule out the possibility of signing goalkeeper Victor Valdes.
Manchester City boss Manuel Pellegrini says he is confident that England goalkeeper Joe Hart will sign a new contract.
The Chivas USA player, who has won 16 full caps before his 20th birthday on Friday, has been utilising the Major League Soccer close season to sample life at Celtic's Lennoxtown training complex.
"I know the history," Agudelo told STV. "It's basically a religion for many.
"Just to have that there and have the support of the whole city would be lovely. Especially due to the fact they are consistently Champions League. Being in the group stage of the Champions League is huge.
"We'll see. I'd have to consider a lot of things but definitely, Celtic is a great club.
"This kind of move has been on my mind for as long as I can remember playing soccer. Going and playing in Europe is what I would like to do. This is, right now, where the best football is being played. I would love to play here."