The 31-year-old is without a club after being released by Sunderland, and had been linked with a return to Portman Road over the weekend.
The club's manager told reporters: "It's never even crossed my mind. I think Titus Bramble will have other options, and probably Premier League options.
"I can't say no, though, can I? That would be a complete lie. What if he came down here and said, 'I love living down here, this is where I come from, what's your budget and what can you offer me? 500 quid, I love it here and I'll come and play'.
"I might consider it then under those circumstances, so if I actually said no I'd be lying. But have I spoken to him, his agent or considered it? No, I haven't."
Bramble spent his youth career with Ipswich, before spending four years with the senior side ahead of his transfer to Newcastle United in 2002.