It is believed that the Cherries tried to sign Beavon ahead of the weekend encounter against Chesterfield, with a view to making the signing permanent in the January transfer window.
The asking price of £25,000 is too much for the Cherries.
On his search for a striker, Quinn is quoted in the Bournemouth Evening Echo as saying: "I've made three or four enquires and I asked about Scott McGleish who went to Northampton. Decent strikers are at a premium and when any become available, there are always clubs after them. I made an enquiry about another couple of lads but the clubs in question are looking for money for them. They put these lads on the list but as soon as you ring up and ask about them, they are looking for money. We want to get people in but at the right price".
On the Beavon situation, Quinn is quoted as saying: "Stuart is a good player, but Weymouth are asking too much for him. They want to get him off the wage bill, but we can't pay a fee".