The paceman has been struggling with an ankle niggle on tour and sat out the final T20 against England and the subsequent two-game short-format series against Ireland.
The 27-year-old then missed a four-day warm-up match against the England Lions as a precaution but Elgar is expecting his pace spearhead to be ready come the first ball at the Home of Cricket.
Rabada has been England's nemesis in the past having taken 52 wickets in nine Tests at an average of 25.80, including career-best figures of 7-112 in Centurion in 2016.
The Proteas skipper said on Tuesday at a rainy Lord's: "KG has done really well the last few days. I think he is very close to being fully-fit. It's looking pretty good for us.
"He will have a bowl in the indoor nets if need be. If he has to do something today, and I'm sure they will push him, but if they feel that he doesn't have to do extra work, then you will most probably see him in the final XI."
England, under captain Ben Stokes and new coach Brendon McCullum, have won their last four Test matches at home playing a refreshing attacking brand of cricket termed 'Bazball'.
While Elgar did not want to coin the new phrase in his pre-match press conference, the Proteas skipper believes his side have the weapons and firepower to counter the hosts.
"I think one of our biggest strengths as a Test side over the last period has been our awareness to adapt," Elgar said.
"I think when you're under the pump in Test cricket you need to have that quality and that skill.
"I think we fast-tracked that at quite a good rate just purely out of the guys having a good attitude around that.
"I think that's going to be a massive factor for us in this series, especially if England do have a flier, which I know somewhere they're going to have periods in the game where they're going to be on top of us.
"We're going to have to find a way to adapt into that situation.
"There's been a lot of learnings from watching what happened in those series and I do think we're a smarter side and adaptability is a big thing for me."