Thordarson faces competition from League Two rivals Boston Utd for the 32-year-old striker, but is not keen on hanging-around while the Frenchman makes his decision on the possible loan switch.
"I will not be hanging around and I have spoken to other players so they have to make up their minds," Thor told the Nottingham Evening Post.
"Eugene is a powerful lad with good experience and is a player who can do the job we are after. But I am not going to wait longer than this week because I need players in before Saturday."
The County manager remains confident he can nabb his principal target - Stoke City's Bruce Dyer - but, with strong competition from Plymouth Argyle and Blackpool, he is now looking at other options as he seeks to bolster his thread-bare strike-force.