The Cottagers risk losing the 26-year-old defender, who can sign a pre-contract with a foreign club from January, on a free transfer in June.
Tottenham remain interested in the centre-back but are prioritising a left-footed option in January. Monaco could make another approach, having had several bids rising to £8.5million rejected during the summer.
Adarabioyo is focusing on rebuilding his fitness before deciding on his future, having just returned to action following groin surgery in September. He has made two appearances in the Premier League this season, both from the bench.
Head coach Marco Silva, who signed a new three-year contract in October, has a positive relationship with his defender, which could offer a pathway to future talks.
Meanwhile, Fulham are ready to spend big in January, prioritising a striker, with Stuttgart's Serhou Guirassy and Wolfsburg's Jonas Wind among those being looked at.