The Belgian keeper was in Glasgow this week as Lennon stepped up his search for a new number one ahead of the big kick-off but, after being given a tour of Lennoxtown, returned home without a deal being done.
Having lost Fraser Forster back to Newcastle after his loan deal expired at the end of last season, Lennon is keen to recruit another keeper to compete with Lukas Zaluska and Dominic Cervi for the gloves – but his chances of landing Stijnen seem to have diminished after he entered negotiations over a possible move to Serie B.
Stijnen's agent Renee Goyvaerts said: "There is an official offer from Sampdoria and we are ready to consider that.
"Playing in Italy would be a good move and there is no problem now that Sampdoria are in Serie B." As revealed in SportTimes yesterday, Stijnen is just one of four goalkeepers Lennon has on his radar, with Stipe Pletikosa and Gregorz Sandomierski joining Stijnen and Forster in catching the Celtic manager's eye.
Pletikosa appears to be the most likely option, with the former Spurs keeper impressing during the Hoops' 1-0 friendly victory over Cardiff City on Wednesday night.
The Croatian is unable to play in Sunday's SPL opener with Hibernian, meaning that Zaluska will start the campaign as the Hoops' first choice – but he could be given the chance to win himself a deal at Parkhead when Wolves visit Glasgow next week for another pre-season friendly.
However, having amassed over 80 international caps during his career, it remains to be seen whether the 32-year-old wants to play another game as a trialist to prove his credentials.
Meanwhile, Katlego Mphela is confident he has what it takes to succeed at Parkhead if he can convince Lennon to take a chance on him.
The Mamelodi Sundowns striker will jet into Glasgow next week for a trial as Lennon mulls over a £1.5million move for the South African internationalist.
Mphela endured a nightmare spell in France with Racing Strasbourg but reckons he has improved enough to resurrect his career.
He said: "Back then I was only 18 or 19 and it was hard to adjust. I ended up coming home, but that has helped me in the long run because I'm now a regular for my country and have played in big competitions like the World Cup.
"I want to go back to Europe and prove myself. It's up to me to show what I can do in Scotland."