Ali's team, which includes collaborator Professor Karl Lyons, will combine biomaterials like collagen with bioceramics, consisting largely of calcium phosphate.
The biomaterials would mimic the cells while the bioceramics would make the compound hard.
Initially the aim was to use the material to fill holes in the way fillings are now carried out but eventually there was potential to grow whole teeth, Ali believed.
He said his team had seen good preliminary outcomes with regenerating soft tissue so were confident it could be done.
Health Minister Jonathan Coleman has welcomed the study, one of 11 groundbreaking projects that have won $1.65 million in explorer grants from the Health Research Council.
"Developing a technique to regrow teeth, for example, is an extraordinary concept and offers huge potential for people suffering dental health problems," Dr Coleman said.
"The Government supports research that leads to improved health outcomes and more effective delivery of healthcare for New Zealanders."
The HRC explorer grants announced today also support other projects such as creating 3D bioprinted vascularised skin, developing a faster way for doctors to detect antibiotic resistance and exploring female infertility.