Mills joined on a season-long deal from Leeds last month after falling out of favour at Elland Road under Peter Reid.
But he is in demand at The Riverside Stadium, with Gibson revealing Boro attempted to buy Mills rather than borrow him in the first instance.
"The long-term objective is to keep Danny," said the Boro supremo. "We would have liked him permanently and we talked to Leeds about that but the deadline was looming and there was no time to complete the deal."
Mills joined Leeds in a £4m move from Charlton in the summer of 1999 and he has since gone on to become a regular in Sven Goran Eriksson's England squad.
However, after publicly criticising Reid over the summer, he is likely to find his Leeds days are numbered.
The full-back, who made his Boro debut in a 3-2 home defeat to Leeds, is likely to command a fee of around £3m should the move become permanent - a move Boro are likely to push forward with when the transfer window re-opens in January.