O'Riley, 25, joined Brighton from Celtic last summer for £25m and immediately struggled to establish himself in Fabian Hürzeler's plans, spending the first half of the season on loan at Olympique de Marseille before returning in January.
He has made a total of 15 appearances for Brighton across the campaign and the club are open to selling for a fee in the region of €15m to €20m.
Borussia Dortmund's coach Niko Kovač and the club's scouting department are understood to be enthusiastic about O'Riley's profile. The Denmark international — born in London to a Danish mother and Irish-American father — operates as an attacking central midfielder and brings a level of technical quality and Premier League experience that fits the profile Book is targeting as he reshapes the squad under the new sporting director's direction.
O'Riley shone during three seasons at Celtic, scoring 13 goals and providing 11 assists in his final campaign at the Scottish club and catching the attention of several top European sides before the Brighton move. The relatively modest asking price reflects his limited involvement this season and gives Dortmund a realistic path to the signing.
Brighton retain a contractual hold over the player until 2029, which gives them leverage to demand a full fee rather than accept a reduced offer. Atletico Madrid have also maintained long-standing interest in O'Riley, according to Sky Sports UK.
Whether Dortmund move first and formally will depend on the outcome of their own summer planning, which must account for a restricted budget following elimination from the Champions League at the play-off stage.