"Last night police caught up with a pair in the Cashmere area. Inquiries are continuing in relation to the man and woman spoken to - and we have not ruled out charging the pair," Nalder said.
"Falsely representing the paintings is an offence and may result in arrest. Obtaining by deception is punishable by up to seven years' imprisonment."
Police said they would be sharing the information with the New Zealand Immigration Service.
"Often the scammers are in breach of immigration regulations. Police will liaise with the Immigration Service who may also take action."
Residents are urged to turn away people selling art at their doorstep.