The striker missed Tuesday's EFL Cup defeat by Norwich with a toe injury but manager Ronald Koeman is optimistic he will be fit.
The Dutchman said: "He did training, separate to the group, today and we expect him to train normally tomorrow morning
If that happens then he is fit for the weekend."
Lukaku's importance to the Toffees was demonstrated against the Canaries, with Everton dominating possession and creating a number of good chances but failing to score.
The Belgian has averaged a goal every other game since becoming the club's record signing in the summer of 2014.
He failed to score in the final 10 games of last season in a dreadful run for Everton that cost manager Roberto Martinez his job.
Lukaku also drew a blank in his first two Premier League games under Koeman but has scored four times in the last two matches and played a significant role in Everton's fine start - they sit second in the table after taking 13 points from a possible 15 ahead of their trip to the south coast
Koeman said: "Against different systems or different ways of defending, you need to be prepared
But it was not the problem that we did not create opportunities (against Norwich)
We did not score the goal.
"The quality players can make a difference in the productivity that we did not have on Tuesday
Before that (we did), and that's important because it's one of the qualities of the players."
Koeman made six changes to the team that beat Middlesbrough last weekend, giving the likes of Enner Valencia, Gerard Deulofeu, Tom Cleverley and Aaron Lennon a chance to impress.
It would be a surprise if any of them forced their way into the starting line-up on Saturday but Koeman did not agree with the spotlight placed on the incomers.
He said: "There's too much focus on these players
What I tried to do was put out the best XI that I thought was the best for the weekend.
"They need to give competition to the rest of the players
Normally we have in every position two players.
"Some had a very good game and some had not the productivity
I was not happy about the result, of course, but I was comfortable with what they showed
It was not good enough because we did not score the goal but in general I wasn't disappointed about the work-rate of the team
"Sometimes you miss chances, that's part of football
In cup football you don't get a second chance
That's a pity but we need to accept it and go on because we have had a good start to the season."
Source : PA
Source: PA