So I just bought a 2009 Infiniti g37x with a 141,000 miles. And every time I push it a little I smell a burning smell coming out of the engine bay when I’m parked. I checked for coolant leaks but I couldn’t find any. I need some help on if I should keep this car or sell it before it gives me major problems.

 

First we need to know what type of burning smell you are experiencing as they could be Oil, Cat's heating up, Plastic, coolant heater hoses leaking etc.

 

It doesn’t smell like burning rubber or plastic it smells like a pot when you first put it on the stove. If you know what I mean? Idk like something overheating.

 

The engine compartment sees 220F easily. First notice if there is any smoke coming from the bay, if there is none proceed to a spirited drive with some high RPM to essentially replicate the issue.
This should make the smell more noticeable and hopefully visible, if everything checks out you could be experiencing debris evaporating from the exhaust. The catalytic converters can easily see 800-1200F which means anything stuck on them or their heat shields will melt.

 

I opened the hood after the drive but I didn’t see any smoke but still smelt the burning smell. And if it was from the exhaust wouldn’t I smell it from the back of the car?

 

Yes and No. If you have any exhaust leaks you'll smell it more from the engine compartment.

 

so is an exhaust leak important?

 

You are going to have to give us a more detailed description about the odor you are smelling. Is it sweet, does it resemble rotten eggs, burning rubber, acrid (irritates nose), etc. Your description that the smell is akin to a "pot on the stove" does not help.

And, yes, a exhaust leak can be potentially dangerous.

 

No it doesn’t smell like anything you named but it most resembles a burning plastic smell if anything.