It helps him get a new contract because it tells the club he has other options and is willing to look at them. If we think he's nailed on to sign, we'll offer worse terms.
I remember Ian Taylor coming out years back under Gregory and saying something along the lines he wasn't happy with being on a lower wage than other players because of his loyalty to Villa and if they took this piss, he'd be forced to look at other options. Shortly after, he got a much improved contract. It's the same sort of thing, except Downing is much more likely to call Villa's bluff.