The Mexican's proposed move to Al Ittihad stalled earlier this week, but Allardyce still expects the deal to happen with Porto and Racing Santander reportedly interested.
"I still remain hopeful that Jared Borgetti will leave us and maybe something can happen in the Middle East," added Allardyce.
"There is a lot of interest in Jared and I have no doubt a deal will be done over the coming weeks with a club somewhere in the world.
"A good number of clubs want to sign him and it will happen soon."
Meanwhile, Bolton lost for the third time in four pre-season outings as they went down 3-2 to Recreativo Huelva in Spain. Kevin Nolan struck twice for Wanderers, who had weakened team due to injuries.
Three adsentees from the match included Kevin Davies, Joey O'Brien and Henrik Pedersen who are all in danger of missing the start of the season.
"Kevin Davies, Joey O'Brien and Henrik Pedersen are all major doubts ahead of the opening league game of the season," said Allardyce.
"As it stands now all three, along with Ricardo Gardner (knee) who is out until at least the end of October, could be out of my plans for the Spurs game, which is a major problem."