Agents for Real and Odegaard have been touting the player's availability for next season after Castilla's failed Segunda B promotion playoffs campaign.
Odegaard's camp refuse to tolerate a third season in Segunda B and are actively seeking a move for the Norwegian teen.
Tribalfootball.com has been informed Liverpool, via intermediaries, have asked about Odegaard's situation and to be kept informed of his plans.
Klopp has attempted to sign Odegaard in the past, having the youngster train at Borussia Dortmund as he considered his options as a Stromsgodset player.
"Jurgen Klopp even spoke with me," revealed Odegaard at the time. "He introduced me to the club, told me what Dortmund think about me and the sporting opportunity they can offer me."
The youngster also stated: “Liverpool have always been my dream club. But I will not let this affect my decision when I choose a new club."
Liverpool are already in contact with Real about Mateo Kovacic, as has been revealed by Tribalfootball.com's Emanuele Giulianelli this week. And a conversation regarding their plans for Odegaard has also been held.
It's been suggested a decision could be made before Real re-assemble for the start of preseason training.