The storm will bring strong winds, particularly in Southland, Otago and Canterbury, where northwest gales could become severe from Tuesday night.
Significant spillover was also expected from the Canterbury and Otago lakes and rivers, along with thunderstorms.
The front starts to move north on Wednesday and will bring some wild weather to the North Island from Thursday, Mr Little said.
Weather warnings might be put in place closer to the time.
The rain would ease to showers on Friday and should blow out by Mother's Day for the North Island - but some South Islanders might not be so lucky, he said.
The West Coast and far south of the South Island will have a "brief reprieve" at the end of the week but Sunday will bring more rain, he said.
"Looking towards Mother's Day on Sunday it does look like we have a return to northwesterlies again and much of the eastern parts of the country are looking dry and fairly mild...but unfortunately down south is looking fairly wet again by then at this stage.
"But obviously it's a long way out. It's a number of days away."
Before the storm reaches the North Island the northwesterlies will likely push temperatures up in some eastern regions on Wednesday and Thursday, Mr Little said.
Temperatures on the east coast of the North Island might even reach the mid 20s, he said.
"So it's not all horrible weather, some folk will obviously be quite happy if it's pushed into those temperatures."