The 23-year-old, who is determined to join Bayer under the cross, has told club officials he wants the switch to go through, leaving Bayer Leverkusen to finalise terms with Strasbourg before the deal can be completed.
Kicker reports that Leverkusen are willing to pay around €30m for the defender, having seen the French club's initial demand of €50m as a non-starter. Since Bayer remain locked in negotiations with Strasbourg rather than walking away to pursue alternatives, the report suggests the asking price has already come down significantly, with an agreement in the region of €35m now viewed as realistic.
Doué, the older brother of Paris Saint-Germain forward Désiré Doué, has been Leverkusen's clear target for the position after head coach Carles Martínez identified none of his existing right-back options - Arthur, Lucas Vázquez and Axel Tape - as an ideal long-term solution.
The Ivory Coast international, who featured in all four of his country's matches at this year's World Cup, made 34 competitive appearances for Strasbourg last season and contributed nine goal involvements.
He has reportedly sought out the opinions of former Leverkusen players before agreeing to the move, and is regarded as a modern full-back with strong offensive instincts and game intelligence.
Leverkusen's finances have been boosted by Thursday's sale of Exequiel Palacios to Ipswich Town, a transfer whose proceeds can be reinvested in full given the midfielder had been fully written down on the club's books after six and a half years at the BayArena.
That windfall gives Leverkusen extra room to close the gap with Strasbourg before Tuesday's 8pm deadline, with a right-back long identified as one of the few remaining gaps in an otherwise settled squad.
Sporting director Simon Rolfes has been driving the pursuit alongside Martínez, with the club also chasing former winger Moussa Diaby's return from Al-Ittihad on the opposite flank in the closing days of the window.
Both deals depend on Leverkusen finding agreement with clubs holding out for higher fees than the Bundesliga side are prepared to pay, but with only days remaining before the deadline, momentum on Doué in particular appears to be building following his personal assurance that he wants the move to happen.