The gaffer missed out on the £8.5million signing of Andy Johnson who opted to sign for Everton, but still has the money and is keen to get someone in as soon as possible.
Saviola has now emerged as a target and the player's agent has confirmed Bolton along with Arsenal are keen.
"There is a proposal from Panathinaikos, as there are from other teams. One of them is Arsenal, while there is also interest from Bolton," Alfredo Kamprera told Greek sports daily Sport Day.
"Our priority is for Javier to remain in Spain or go to England, because he is interested in the quality of the football. Greece is not first choice as the league is not the same quality as in other countries."
Saviola impressed during the World Cup with Argentina and Allardyce fears his performances may have hiked his price up too much for Wanderers.
Meanwhile, Sam Allardyce, whose only summer signing to date is the Israeli international midfielder Idan Tal from Maccabi Haifa, is now running the rule over two Spanish trialists.