Gilmour would be a shoo-in for the Scottish Premiership champions, and would no doubt gain a lot under the tutelage of Gerrard.
It's thought that while Chelsea boss Thomas Tuchel is a huge admirer of Gilmour, he is willing to let him go out on loan for the season as he doesn't feel the Scot is ready to be a first-team regular.
Premier League new boys Norwich are also interested in the midfielder.
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!