There is still an expectation that they will add another centre-back and forward.
Ange Postecoglou has been linked with a move for Moroccan forward Ryan Mmaee. The Ferencvaros striker scored 17 goals last season.
Recovering from an ankle injury which kept him out of the run-in, the 24-year-old will be hoping to represent Morocco at the World Cup.
The Hungarian giants have all but ruled out a possible move.
Ferencvaros sporting director Tamas Hajnal said: “We are waiting for him to help us when he is in good condition. It is almost impossible for him to leave before the World Cup in Qatar at the end of the year."
One player linked with a Celtic Park move who will definitely not be making the switch to Glasgow is Japanese defender Ko Itakura.
The 25-year-old has joined Borussia Monchengladbach, signing a four-year deal with the Bundesliga side.
A live option is Malick Thiaw, Itakura’s former team-mate at Schalke 04.
With a reported price tag of £8million, Celtic and AC Milan have been credited with an interest in the German Under-21 international.
Speaking to WAZ, Schalke’s sporting director Rouven Schroder expressed their desire to keep Thiaw but left the door open for a possible transfer.
He said: “We have always said that we will deal with offers that come in. If the overall theme fits, we’ll also think about it.
“Malick is here and I think he suits us very well in the Bundesliga. Nevertheless, he is of course in demand because of the under-21s and his performances.”
Meanwhile, one transfer all Celtic fans would like to happen is the signing of Jordan Larsson, son of club legend Henrik.
The 25-year-old is a free agent after leaving Spartak Moscow.
Due to the situation in Russia and their invasion of Ukraine, Larsson spent time with AIK Solna earlier this year but the Swedish club have revealed they are unlikely to sign him due to interest from bigger clubs.
“He has delivered at a level here that is above the Allsvenskan and that opens doors,” sporting director Henrik Julius told Aftonbladet.