Albion tried to sign the versatile left-sided player in the summer, but had four bids ranging between £9million and £12m rejected by the champions.
Even though Schlupp was keen to come to The Hawthorns, the Foxes wanted to keep hold of as many of their title-winning squad as possible.
However, Schlupp has struggled to get minutes under Claudio Ranieri this season and sources close to the frustrated 23-year-old say he wants to join the Baggies in the New Year.
Schlupp has only started one Premier League game so far this campaign, and featured just once in the Champions League so far.
Ranieri has been playing £16m signing Ahmed Musa on the left wing, and the Italian also bought 19-year-old left winger Bartosz Kaputska in the summer.
Schlupp fears his chances will become increasingly rare at Leicester and is hoping Albion re-kindle their efforts to sign him.
Earlier this month, Baggies boss Tony Pulis didn't rule out a renewed attempt to sign Schlupp in January, but he's wary of Leicester playing hard-ball again.
When asked about the Ghana international prior to Albion's game with the Foxes, he said: "He played (in the Champions League) so I don't see him being sold if he is in the team."
Schlupp can play either on the wing or at left back. Although Pulis is happy with his options at left-wing following Chris Brunt's return from injury and James McClean's impressive start to the season, he is still after a left-back.
Everton loanee Brendan Galloway may return to his parent club in January, having failed to keep his place in the starting line-up.
Allan Nyom is playing at left-back at the moment but his preferred position is right-back.
And the Welshman is hoping to inject some youth into his ageing squad. "We need to bring some quality in," said Pulis.
"I've spoken to the Chinese owners, and that's what we'll try to do. I've put something towards them.
"We're an older team and we need younger players with more quality to come in and help the group."