The former Liverpool midfielder has become available after agreeing to the mutual termination of his contract at Paris St Germain.
Reading were among the first to express an interest in acquiring the 28-year-old's services, with contract talks and a medical being held.
No agreement has been reached, though, and discussions have been brought to a close.
Adkins said in the Reading Post: "That's not going to happen."
While he may have been forced to concede defeat in the pursuit of one top target, Adkins has refused to rule out further movement on the transfer front - with reports suggesting that the Royals are looking to strike a loan deal for a striker.
Adkins added: "If something materialises that we believe can benefit and enhance the group then we'll be very active.
"But at the moment we're working hard with the group we've got and our focus is on the next game, which is against Leeds United."