Former Celtic midfielder Kris Commons has questioned the wisdom of the club signing German defender Marvin Compper.
The 32-year-old centre-back will join the Scottish champions in early January after signing a two-and-a-half year deal to move from Red Bull Leipzig.
But Compper will be ineligible for Celtic's Europa League tie against Zenit St Petersburg in February, having played in this year's Champions League.
"I find it strange Celtic have signed a defender who is 32," said Commons.
"When they are over 30, there are a few doubts in terms of 'how long have they got?' and their fitness levels. Is he going to be sharp enough? He is a big boy.
"He is not able to play in the Europa League, and I think that is where they need him. Go and get a centre-half who can take you to the next level.
"Hearts really put the fear into the Celtic back four last Sunday and it was the sort of performance that European teams do to Celtic, putting them under pressure.
"They played in all the wrong areas, and individual mistakes cost them, especially in central defence.
"There was evidence that a centre-half needs to come in, not necessary to play, but to put pressure on the players there. Dedryck Boyata, Jozo Simunovic, Erik Sviatchenko - they must be thinking 'I need to up my game and concentrate on what I am doing, with and without the ball'.
"Celtic need an experienced defender for European competition, but this guy coming in is not eligible to play in Europe. And he is 32. How long is he going to play? Three years? If he doesn't hit the ground running, they are going to be looking for a new centre-half in the summer.
"I think they need to go for a player who is playing at a good level of football, who is between 25 and 28, that has good experience and knows what the club is all about. He can play in Europe and slot straight into the team. Compper is 32, going on 33, so there has got to be a slight risk there."
Manager Brendan Rodgers said on Thursday that he hopes to add "one or two more" new players in time for Celtic's warm-weather training camp starting on 6 January, when Compper will join up with the squad.
BBC Scotland understands Rodgers may try to sign a second centre-half, with Boyata, 27, entering the final year of his contract in the summer, and no guarantee the Belgian will sign a new deal.
"Every single transfer is a gamble, but you try to eliminate the gamble," Commons told BBC Sportsound.
"Who knows, Compper might be superb in the next three years and be an unbelievable signing.
"But Celtic need a centre-half for European football, someone who is going to get you through these next two ties [against Zenit].
"They may well bring in another centre-half, but you can't keep four or five international, fit centre-halves happy. It is impossible. So it looks like one or two might be leaving."