Would you sell to someone with no feedback?

I would not sell if person was not located in my country.
I would ask if they had any feedback from other sites which I could view.
I would need to speak with them on the phone a couple of times first, to get a sense of their genuine interest and valid identity.
I would accept payment only via Paypal.
I would make it clear who is responsible for what actions to be taken were the item damaged in shipping or otherwise not properly functioning upon arrival.

I'll sell if I get money.
Had few problems with international sales when paypal tried to 'favor the buyer'. I called back and explained them that several countries may hold items in customs indefinitely and repossess for reason or no reason which I'm DEFINITELY not responsible for and got funds back. First time they told they're doing it as 1 time courtesy, but this courtesy happened more than once after some line of unpleasant conversations.

Local sale is always better, but done plenty of international sales and continue doing that. 

There are two issues, one is payment (and using Paypal mostly solves that issue) but the other issue, which is just as important to me, is whether the individual can be depended on to deal with you reasonably.   People with positive feedback at least have a track record of working well with others.  If the feedback includes both buying and selling, and transactions for at least a few higher priced items, to me that is even better.    

You already received some good advice from rockadanny and I would add that, for me, the desire to deal with somebody who has no feedback would also depend on the value of the item I was selling.  I am inclined not to sell big-ticket items to folks with little or no feedback and I state that in my ads. Selling a pair of $200-300 cables is one thing but selling a $5-10K amplifier is something else entirely.  I should add that I won't purchase from sellers who have no feedback because of the same types of concerns.

My advice to those without feedback would be to start by buying a few lower priced items simply for the purpose of establishing feedback here.

Are multiple offers flowing in ? I assume not . How long have you had the item for sale ? Along time , Then i might be more apt to selling to someone with no feedback. If a basic ad you have no way of speaking with them on the phone . I would try and get some dialogue going via messaging . If they are replying with short answers you might get a vibe. Thats how i would go about it .

" What precautions should I take before accepting the offer and posting the item???"

Don't take Paypal and don't ship outside the 48 states. Other than that, make sure you get paid first before shipping the item.