The 30-year-old is yet to drop a set in Stuttgart following her return from a 15-month doping ban and saw off the spirited challenge of Estonian qualifier Kontaveit 6-3 6-4.
The ranking points Sharapova has collected mean she is already close to rejoining the top 250 on Monday, and victory in the last four on Saturday would guarantee a spot in the top 200.
That would be enough to earn her entry into the qualifying tournament at Roland Garros without the need for a wild card.
The French Tennis Federation will announce whether the two-time French Open champion has been awarded a wild card into the main draw on May 16.
After an understandably shaky start in her first match against Roberta Vinci, Sharapova has looked more and more like her old self.
Kontaveit, ranked 73, appeared a kind draw for a last-eight clash but the 21-year-old has been in fine form and knocked out French Open champion Garbine Muguruza in the second round.
Kontaveit was not afraid to go toe to toe with Sharapova but, from 3-2, lost five straight games in a barrage of powerful hitting from the Russian.
Sharapova took control of the second set early and, although Kontaveit threatened a comeback, ultimately she could not get back on terms.
After breaking when Sharapova served for the match, Kontaveit had the chance to level but Sharapova stepped up once more and took her first match point with a thumping return.
Speaking in an on-court interview on BT Sport, Sharapova, who next faces either Carla Suarez Navarro or Kristina Mladenovic, said: "I thought I had a really good rhythm.
"When you don't know your opponent too well, the first six games we were trying to figure each other out but holding serve quite comfortably. When I got the opportunity I felt I really rolled with it and gained confidence from it."
If Sharapova can build on the form she has already shown, it is certainly not impossible she could win a third French Open title.
That would be a remarkable story following on from Roger Federer's extraordinary Australian Open success after six months out injury.
Sharapova said: "What he's done is amazing and obviously you want to follow in his footsteps and obviously I would love to have the type of comeback he's had."
Read the original article on Eurosport: Sharapova closes on French Open qualifying spot after reaching Stuttgart semis