The 25-year-old free agent, who played in all three of Poland's Euro 2012 games last month, took part in only a handful of matches for Werder Bremen last season.
But the left-back believes he has the CV to show what he can do, and along with Celtic, a clutch of clubs – including Newcastle – are tracking him.
Bremen offered Boenisch a new contract, but he was not happy that he was given so little game time last season and rejected the deal.
When Celtic boss Neil Lennon was asked after last night's 1-0 defeat to Stuttgart Kickers if he could be about to offer Boenisch the chance to join his squad on trial, he said: "There's a possibility of that happening, but I haven't heard yet from his representatives.
"Until we hear, there's nothing we can say."
However, today Boenisch made it clear he will reject any such offer, and said: "I won't go for a trial. I am not a youth team player. They could see me play during the Euro Championships."
Celtic are also on the trail of Republic of Ireland Under-21 full-back Aidan White, who has concluded his contract at Leeds United.
"He's a possibility again," said Lennon. "He is a player who interests us, but that's as far as we have taken it so far."
Lennon is also trying to progress his search for another striker, something which was already high on his list of priorities before they failed to find the net in either of their opening two games of this pre-season tour.
The manager refuses to panic, even though the Champions League qualifiers are just over two weeks away.
Lennon said: "I would like to see more of a threat in front of goal, although it's been mix and match for us over the first two games.
"The boys who were given a bit more of a break because of international commitments will integrate.
"The likes of (Victor) Wanyama, (Mohamed) Bangura, (Mikael) Lustig and (Adam) Matthews should be up and running soon, and that will make us stronger."
Lennon also reported Matthews has not played any part in the two matches due to a calf injury.
Overall, the manager is content with the progress he can see.
He said: "There is rust there, and I understand that.
"However, I expect a little bit more, although there's no need to get angry with them.
"We're concentrating on games three and four now.
"It's still very early for us, and I felt it was a very good workout.
"The one disappointing thing from my point of view was our play in the final third. We didn't work the goalkeeper enough.
"However, we're coming on well enough. We want to step it up for our game tomorrow and then Saturday against Ajax.
"There will be a lot more football and less conditioning now."