The 29-year-old winger arrived to Stamford Bridge from Russian outfit Anzhi Makhachkala in the summer of 2013 after the Blues beat Tottenham Hotspur to his signing.
The Brazil international quickly became a key player for former manager Jose Mourinho at Chelsea and rumours linking him with Manchester United have been a regular occurrence ever since the Portuguese boss succeeded Louis van Gaal at Old Trafford.
Willian himself recently admitted that in the summer he held talks with United about a potential transfer as Mourinho was then on the hunt for a winger.
Willian also recently had to take social media to deny speculation linking him with a return to his homeland to play for Palmeiras.
But the uncertainty over his future at Chelsea remains with the Brazilian having only started eight Premier League games during the opening half of the season.
However, Willian has told fans to be "calm" after ruling out the possibility of moving elsewhere in the upcoming window.
"The fans can be calm [about me leaving]. I am a Chelsea player and I am very pleased with the way I have been playing in recent weeks," Willian said, as quoted by Evening Standard after scoring a goal in the Blues' 3-1 win over Huddersfield Town on Tuesday night (12 December).
"When I play I always try to do my best. I try to help the team to play well, to score goals and make assists. Against Huddersfield I did that with my team-mates."
Willian, however, refused to throw in the towel just yet with Chelsea now 11 points behind Manchester City but with one game in hand.
"I feel sad because we lost these (three) games. The team that wants to be champions can't lose these kind of games. We know we didn't play like we usually do. We didn't play these matches very well because we made mistakes and the opposition scored goals," Willian added.
"Am I frustrated because the gap should be closer? Yes. It is a big gap but we have to fight until the end. There are a lot of games to play and anything can happen. We will never give up. We have to always continue."