The youngster, who can turn out at centre-back or right-back, has made three Premier League appearances this season and two more in the cup competitions.
His only start came in the 4-0 FA Cup win over Preston North End earlier this month, slotting in at full-back against the Championship side.
The Standard report that there is loan interest in Gilchrist this month but Chelsea intend on keeping him around the first team as they continue to deal with a string of injuries.
Fitness problems have plagued Mauricio Pochettino’s squad this season and continue to do so, with a number of players sidelined.
The Blues are next in action on Tuesday in the League Cup semi-final second leg against Middlesbrough and will be without Wesley Fofana, Reece James, Marc Cucurella, Romeo Lavia, Christopher Nkunku and Robert Sanchez through injury, while Nicolas Jackson is away at the Africa Cup of Nations.
Gilchrist came off the bench in the first leg at Middlesbrough, which Chelsea lost 1-0.
The report states that Chelsea are open to loaning out other youngsters, with goalkeeper Lucas Bergstrom, full-back Dylan Williams and defender Zak Sturge all available this month.
On potential arrivals at Stamford Bridge in January, Pochettino told Sky Sports last month: ‘The Sporting Director and us, we are always talking and assessing – if we need to do something, we’ll be ready. The pressure is always to bring young talent, and we have different types of targets – with experience, without experience, some younger than others and that’s what it takes to provide the team with what it needs.
‘We need to be open to describing the situation. Always communication is really good with the owners, we’re sharing everything. It’s about sharing ideas; we need each other to express our vision in a way that’s a positive statement for the club.
‘If we need to add, we do it together, in a way that takes the best decision for the club.’
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