The fast bowler missed the Proteas' final T20 against England due to an ankle injury and was not risked during the four-day warm-up match against the England Lions at Canterbury last week.
"I hope (he will be fit). He's come on well I think," Boucher said.
"The one concern is always maybe his loads, but he's a great athlete so his body seems to have recovered nicely and he's not feeling too much pain.
"He'll have probably his final test today to find out how he's going but I'm hoping that he pulls through, Rabada is a massive player for us as we all know so for him to be part of the final XI would be very special for us."
Boucher's squad have been soaking up the history at the home of cricket, including a visit to the Lord's museum, ahead of the first Test match against England which starts on Wednesday.
The Proteas have not travelled to England for a Test series since 2017 and for many players in the squad it will be their first taste of Test cricket in England.
Boucher admitted emotions were running high ahead of the occasion.
"When the guys arrived and walked into the museum - we were very privileged to have a trip to the museum - and all the players just staring in awe of what was around them," Boucher said.
"So just watching the players' reaction walking into Lord's. There's a lot of passion and emotions are running high in a good way.
"So as a coach you don't have to try and get the boys all g'eed up for a game like this, I think that's already there.
"So I think that the youngsters want to be here and they want to perform at this ground.
"They want to be a part of hopefully creating something special and become a legend in the game like a lot of cricketers in the past have been."