Rodgers has a particular problem in central defence, where he has been forced to deploy Nir Bitton, Kristoffer Ajer and occasionally Kieran Tierney as makeshift centre halves in recent games.
Dedryck Boyata is out injured until at least October, Jozo Simunovic is fit but a little injury prone, and Erik Sviatchenko appears to be third-choice at best.
The pursuit of, and eventual collapse of a deal to bring South Africa international defender Rivaldo Coetzee to Parkhead in the final week of the transfer window suggests that Rdogers was, and perhaps still is, keen to bring in defensive reinforcements.
Although the Celtic manager has stressed that he is targeting ‘quality’ signings, he may feel an extra body capable of playing in defence - who isn’t a defensive midfielder by trade - would be advantageous.
Here are five free agents Rodgers could bring in...
Last club: Lekhwiya (Qatar). Age: 30
The Spaniard signed for Swansea City in July 2012, shortly after Rodgers had left for Liverpool. He went on to make more than 70 appearances for the Swans, with whom he won the League Cup in 2012, before joining Lekhwiya in the Qatar Stars League in August 2014 - linking up with boss Michael Laudrup for a third time.
He left Qatar at the start of July with one league title under his belt, and six goals from 60 appearances.
As well as Premier League experience, he’s made ten Europa League appearances and has experience of playing in both the Spanish and Italian top flights. However, wages could be an issue depending on what he was getting paid in Qatar.
Last club: Norwich City. Age: 31
Paris-born Bassong has a wealth of top level experience, having made more than 170 Premier League appearances for the likes of Spurs, Norwich and Newcastle as well as playing 42 Ligue 1 matches in France.
The Cameroon international has been capped 16 times and appeared at the 2010 World Cup.
In terms of European experience, he’s faced the likes of Real Madrid and Inter Milan in the Champions League, and also played in the 0-0 draw with Hearts at White Hart Lane in the Europa League qualification rounds in August 2011.
Currently training with Birmingham City, Bassong is unlikely to be offered a permanent deal at St Andrews and, given he’s still only 31, could provide some much needed cover at the back for Rodgers.
Last club: Celtic. Age: 36
More than 350 EPL appearances and a staggering 67 Champions League appearances speak for themselves. Rodgers brought Toure in last season on a one-year deal, and he made 17 appearances including six in Europe.
Although Toure was released by Celtic at the end of his contract, Rodgers said during the summer that he hadn’t ruled out bringing the Ivorian defender back in a player/coach role. Since then, Toure has gone on to take up a role with the Ivory Coast Under-23 side but has had no firm offer from Celtic.
He would be a safe acquisition given his vast experience, Rodgers knows exactly what he’ll be getting and the likes of Ajer and Anthony Ralston would no doubt benefit from his guidance.
Whether or not he chooses to solely focus on his coaching role at international level remains to be seen.
Last club: Rotherham United. Age: 32
Another Celtic old boy, Wilson had initially joined the Hoops from Nottingham Forest, and he returned to the City Ground in August 2013 after just over two years at Parkhead.
In August 2016 he joined Rotherham, but made just eight Championship appearances as he struggled with injuries before being released following the Millers’ relegation.
He held talks with Neil Lennon about a move to Hibs during the summer which would suggest he’s not entirely against the idea of playing in Scotland again.
He also has experience of playing for Celtic in Europe, and if there are no underlying concerns about his injuries, could be a good fit short-term.
Last club: Ternana (Italy). Age: 30
This would be a bit of a risk, but Celtic do have something of a history of unearthing unlikely gems - although they’re not usually 30 years old.
His 14 appearances in the Europa League - against the likes of Villarreal, Atletico Madrid and Sporting CP - would stand him in good stead for European fixtures, but most of his club appearances have come in Italy’s top two leagues.
While he has made over 100 appearances in Serie A for Lazio, Fiorentina, Sampdoria, Frosinone and Cagliari, his handful of appearances elsewhere - eight in England, a couple in La Liga - suggests that he may be more suited to the Italian game.