The Japanese trialist - who celebrates his 25th birthday on Friday - could be invited back after the New Year.
Neil Lennon and his management team will take the next few days to consider whether or not it is worth pursuing their interest in the Jubilo Iwata captain.
Yamada spent last week at Lennoxtown trying to convince them he would be a useful addition to the squad.
But assistant boss, Johan Mjallby, admits the lack of any game time has meant it has been difficult to assess the attacking midfielder with the lethal shot.
He has now been sent home for the festive period, during which Celtic have a heavy fixture schedule which will reduce training to a minimum.
But Mjallby expects a decision on what happens next will be made during this time. He said: "I think Hiroki is going to go home for Christmas and New Year. Obviously we need to sit down and make a decision about him.
"He has done okay in training, but it is always hard when you don't see them in proper games. In an ideal world, you would have a bounce game where you could see him in action when proper tackles are flying in. But he looks okay and he is going to be in our minds."
If Celtic do decide to make Yamada the third Japanese Bhoy to join the club, after Shunsuke Nakamura and Koki Mizuno, they can expect a fight from Jubilo Iwata.
The team recently relegated from the J-League believe they have Yamada under contract for a further year and have indicated they would look for a transfer fee.
Mjallby is content to leave that side of things to others, but reckons the very fact Yamada was able to come to Scotland and train with the Hoops indicates he would be available for free.
The Swede said: "I don't know the situation. But the season is now finished in Japan, so I would say that, if he is on trial, he is probably out of contract."
Definitely on his way back to Lennoxtown is Mo Bangura, who will become eligible to play for the Hoops again when they meet Partick Thistle on New Year's Day after completing his year-long loan to Elfsborg.
New signing, Icelandic striker Holmbert Fridjonsson, will also finally come into contention for his debut having joined on a pre-contract from Fram.
And it would appear Tony Watt could also be back at Lennoxtown five months ahead of schedule after Lierse coach, Stanley Menzo, indicated the striker's poor attitude will mean his loan spell in Belgium is cut short.