The 28-year-old midfielder is a free agent following the cancellation of his contract by Paris Saint-Germain.
Reading have held talks with the former Liverpool man but Adkins has said that nothing has been finalised.
He told the Reading Post: "A player of great quality has been highlighted as available for us to pursue and we've gone and pursued it.
"Like everything, you have to do the right due diligence in respect of medicals and then you have to make a take on it as to what is the right business to do for the club.
"There was a genuine desire to try and get it done. Unfortunately, there was a situation where both parties couldn't come to an agreement. Now the scenario is the player is out of contract. The fact is that at the moment a deal has not happened, that's not say it won't in the future."
Sissoko made 34 appearances in two years with PSG.