Leicester’s win over Chelsea on Monday evening has lifted them into top spot in the Premier League, and there is now genuine hope that they could claim a Champions League qualification space at the very least.
The Foxes will have to decide whether to spend big in January and really try to announce their intentions of claiming a top-four place, or to stick with the players that have got them into this position in the first place.
And Carragher said: “The January window is a difficult one, do they think: 'We have a right go at this to guarantee top four or even have a run at the title?'
"But could bringing in signings upset the apple cart? It seems such a settled team and they all know what they are doing, so it could be an awkward month for them."
Leicester beat Chelsea 2-1 at the King Power Stadium last night to extend their marvellous start to the campaign.
Claudio Ranieri has done a miraculous job since taking charge of the Foxes, and they are flying at the moment.
Both Jamie Vardy and Riyad Mahrez got on the score-sheet against Chelsea, and even though Loic Remy struck a late consolation for the visitors it was not enough.
Leicester are currently 20 points clear of Chelsea, and nine points away from fifth placed Tottenham Hotspur.