The Dutch international midfielder hopes he has done enough during his week's trial at Lennoxtown to be given the opportunity to bring his experience to Neil Lennon's side.
Zenden in now back in Holland to be with his pregnant partner, and expects to hear from the Hoops over the weekend.
Concerns over the fitness of the 35-year-old, who has not played competitively since he left Sunderland in May, appear to have been lifted after his impressive performance in a bounce game against St Johnstone on Wednesday. Now the ball is in Celtic's court as they decide if they want to make a contract offer to the free agent.
That could be for the next two months, or until the end of the season. His father, Pierre – who also acts as his representative – has made it clear his son is not simply looking for one last pay day.
Zenden just wants the chance to resume his career and, preferably, with a team he believes can add to his medal collection.
From Holland, Zenden Snr said: "Boudewijn feels good about Celtic and it is absolutely something he would be interested in. It's not about money. It's about the sporting challenge."
The former Barcelona, Chelsea and Liverpool star believes he has a few more seasons left in him. But his father is still waiting to see what length of contract Celtic are willing to put on the table, if they do decide to invite Zenden aboard.
Pierre added: "To start with, a deal until the end of this season would be okay. It's a good challenge he is looking for, and I think he still has a lot to offer."
Celtic are also expected to make a decision soon on another trialist, left-back Andre Blackman, who set up a goal in the midweek bounce game win.
And they are one of several clubs showing interest in Rosenborg full-back Mikael Lustig.
But the 24-year-old Swedish international admits he does not know where his future lies, and said: "I know Celtic and Fulham are interested, but there's no offer."