The Belgium international suffered a calf strain against PSG in the Champions League but the club are hopeful he can be back in action before the end of the season
The Belgium international was forced off in the first half of the Blues' Champions League second leg victory over PSG in midweek with a calf strain and missed Sunday's 1-0 win over Swansea.
However, speaking after the victory at the Liberty Stadium, that saw Chelsea keep pace with Liverpool at the top of the Premier League, assistant first-team coach Steve Holland was optimistic about Hazard's fitness.
"Eden Hazard should be fit sooner rather than later, we can't say for sure when, but a week's break is good for us," he told reporters.
Striker Demba Ba followed up his midweek heroics with the winning goal at the Liberty Stadium, which keeps Jose Mourinho's men just two points behind Liverpool, and Holland admitted it was a big victory for his side.
"On the back of playing a big Champions League game, this is a very good three points for us," he added.
"This is the fourth time I've been here with Chelsea and the first time we've won. Swansea are good at keeping the ball.
"Demba Ba deserved this, he is often working hard after training on different types of finishing.
"We have to win all of our games left, but we have been facing that ever since our result at Crystal Palace."