Underhill is still on his way back to full fitness after he ruptured a tendon in his big toe while training with England in March.
England boss Eddie Jones is without Nathan Hughes and Courtney Lawes this summer and Underhill is reportedly top of his list for replacements.
Booth has revealed the Bath star is still not 100 per cent and he is worried about pushing him too hard.
When asked if Underhill will be ready, Booth said: "Not as far as we're aware. He would have to accelerate [his recovery] a lot to do that.
"He returned to us broken and he's not set one foot on the training pitch.
"He's still at the rehab stage so I'd imagine he's got a long way to go yet. Everyone knows what international rugby is like and going away to South Africa is certainly not going to be for the fainthearted and the underprepared.
"You need to be at your best for those sorts of tours, so hopefully common sense prevails and they do what is right for England, for us and for Sam."