Collins has been made available by Stoke and is understood to have left their training base in America.
Forest are in desperate need of defensive reinforcements and the centre-half has been heavily linked with a switch to the City Ground.
"I think Danny has been made available by Stoke and there are one or two clubs interested in his services and we're just one of many," said O'Driscoll, who held his first media conference as Forest boss on Wednesday morning.
"He's a good character, he's been promoted twice from the Championship and they are the boxes you need to tick first and foremost."
It has been suggested that former Forest academy graduate Jenas is also among those the Reds will look to bring on board, but O'Driscoll claims no approach has been made for the Tottenham midfielder.
He added in the Nottingham Post: "Again, if good players become available, we will look at things. At the minute, that is just speculation. We have not had a conversation."