Celtic hope to add to their squad this week but manager Neil Lennon is wary of deals being “called off last minute”.
The Scottish champions are reportedly close to a 6m euro (£5.5m) deal for AEK Athens goalkeeper Vasilis Barkas.
And they have also been linked with West Ham striker Albian Ajeti, Peterborough forward Ivan Toney, and Scotland frontman Steven Fletcher.
“I don’t want to tempt fate,” Lennon said after Monday’s 3-1 friendly win against Hibernian.
“It takes a bit of time and they could be called off last-minute type of thing. Hopefully we will have something to get our teeth into this week in terms of bringing players in.”
Goalkeepers Fraser Forster and Craig Gordon have both left the club since last season ended, with Lennon confirming the position was one he is looking to strengthen.
Karamoko Dembele was on target and Patryk Klimala netted twice as Celtic completed their pre-season programme against Premiership rivals Hibs.
Striker Leigh Griffiths, who was left in Scotland to work on his fitness when Celtic travelled to France for three friendlies, featured and Lennon further praised the striker’s improved condition.
The manager said the 29-year-old will be “around the squad” for Sunday’s league opener at home to Hamilton Academical.
“He showed me he has a lot more responsibility, individually and in the team,” Lennon said. “It’s the best I have seen him in 18 months.
“A lot of it is down to personal responsibility, and he knows that.”