My mom's 99 V70 is making a strange whirring noise in the front end - it can be heard very pronounced on the car's exterior. It happens when the engine is on and even if the key is only in the first position and the engine is not on. It happened on a day when my mother says she was pushing the car.
Any ideas of what the problem could be?

Apreciate the replies!

I vote for headlight wiper motor. It is easy to unplug them and see if the noise goes away.
Good luck& Have fun

Aside from a stuck-on cooling fan (relay or temp sensor), some people reported buzzing or vibrating noises from the idle air control valve (Don't know if this component is present in the 1999 models as it was in the earlier ones).

The sound kind of gets more intense once the engine is turned on. As well my mother says when driving on the highway several times she felt a kind of jerk/surge. She also says you can kind of hear a timing sound in it. To me it seems like it is coming from the front end of the car close to the headlight on the driver's side.

There are only two electric motors behind the driver's side headlight, the headlight wiper motor and the cold engine air pump. If the air pump has water in it, it will make noise, but it is only supposed to be operating for the first few minutes after starting.
Turn the headlights off to check for a bad wiper motor with a loose wiper blade. They will short out and run sometimes.
The idle air control motor, just below the throttle body, will make noise when ever the car is on, but it is not speed sensitive.

Klaus
--
1975 164 w/174,800mi (For Sale) 1995 850T w/91,000mi, 1998 V70R w/129,000mi

Sounds like the electric cooling fan is running. Possible stuck or fused thermostat or electrical short to ground.
When you hear the noise, open the hood and see if the fan (plastic fan) between the engine and the radiator is turning.

I am not speaking of a turbo model. Any othe ideas?

could be turbo warmer. not to worry if so.

does it go away when the car is warmed up.

if you do not hear the whiiring in the spring time then its the turbo warmer.

I am not speaking of a turbo model any other ideas?