Not easily possible with this car as Chevrolet didn't offer a V8 in this car.
Never say never though.
With enough money, you could put a V8 in anything.
There would be a lot of fabrication though. Seeing that you had to ask this question to begin with, I will assume you do not have the fabrication skills or resources to do the job yourself.
If I were to attempt this, I would use a front wheel drive V8 setup from another GM product. Maybe a Northstar form a Cadillac.
I would figure on about $5,000 for used front wheel drive engine, transmission, computer, wiring harness, suspension, cooling system, and frame.
Figure on about $100 per hour to pay someone to install them for you. Figure on about 300 hours labor at a cost of $30,000.
Figure on about an extra $2,000 for unexpected extras.
I would figure on about $37,000 - $40,000 to convert your 2001 Impala to a V8.
Wouldn't you be better off just getting a new 2009 Impala SS?