Requiring Associate Health Minister Peter Dunne to approve applications "could be a bit too much bureaucracy", Coleman said.
Dunne is currently reviewing the rules for considering applications for cannabis-based medicines and is expected to report back tomorrow.
Coleman said it was "probably more likely" that the responsibility for approving medicinal cannabis would be delegated to specialists rather than GPs.
"But we'll see," he said.
Coleman was asked about the issue after cannabis law reformists held a rally on Parliament's lawn this afternoon, calling for improved access to medicinal cannabis.
Medicinal cannabis is used to treat a range of conditions such as chronic pain, terminal cancer, Tourette's and child epilepsy. Patients say it reduces the severity of their symptoms.
Just two pharmaceutical-grade cannabis products, Sativex and Tilray, are available in New Zealand. Neither are funded by Pharmac, and they cost users between $700 and $1300 a month.
Prescriptions are approved by the Ministry of Health. Other products must be approved by Dunne.
Delegating approval to specialists will not necessarily make it easier to get access to cannabis products, but it could speed up the application process.
However, it will not solve another major barrier - supply. Demand for pharmaceutical-grade cannabis outstrips supply, and the Government cannot force manufacturers to export to New Zealand.
Prime Minister Bill English said today he believed the "rules were about right" for medicinal cannabis.
Some National MPs were more open to a policy change.
Cabinet Minister Nikki Kaye said her constituents had told her "it is a bit difficult to get access" to cannabis-based medicine.
"Previously I didn't know that much about it and I'm really keen to get more schooled up on it. But obviously I'm really keen to see what Peter Dunne's doing in this area."
Labour leader Andrew Little has promised to legalise cannabis products for medical treatment "very quickly" if he is Prime Minister, but he would not go as far as legalising the drug for recreational use.