Davies damaged a shoulder in their Judgement Day win over Newport Gwent Dragons and will miss their final two regular-season games.
The competition's top four teams will play off for the title in May.
"If we're lucky enough to qualify for the top four then James in a race against time for a semi-final," said head coach Wayne Pivac.
"The injury is improving. He's feeling much better this week but thee things take a little bit of time.
"No surgery required at this stage so hopefully he can rehab and be all right for the semi."
Pivac also believes Davies is a strong contender to go in Wales' summer tour in which they face Samoa in Apia and Tonga in Auckland.
"James has been one of the in-form sevens in the competition. He's had a lot of man of the match awards.
"Within our ranks we rate him very highly, what he can do with the ball, what he can do at the breakdown.
"And defensively he's improved and I'd love to see him go on tour but that's out of my hands."
Scarlets lie third in the table with only three points separating them from Ulster, who are fifth.
The Llanelli-based region are at Connacht on Saturday, 29 April and a week later host Ospreys, who are fourth.
Irish team Leinster are already assured of home advantage in the play-off semi-finals on 19/20 May.
The final takes place at Dublin's Aviva Stadium on Saturday, 27 May.
Scarlets will be without injured open-side flanker James Davies until at least the Pro12 play-offs.