Depay, a £31m ($37.8m) signing from PSV Eindhoven in June 2015, has become something of a forgotten figure at Old Trafford, with the last of his eight fleeting appearances in 2016-17 coming with a late substitute's cameo in a 4-0 Europa League victory over Feyenoord in November. He is yet to start a single Premier League match since Mourinho succeeded Louis van Gaal last summer.
Updating reporters on the latest regarding Depay's situation following a first bid that Sky Sports believe to be worth approximately £13m, Mourinho, speaking ahead of United's clash with fierce rivals Liverpool on 15 January, said: "The latest is that the offer that we've had is far from being reasonable for us. At the moment, he's our player and if in the end [of the window] nothing happens, he is one more option for us."
With strong links to Everton fading somewhat and reported interest from the likes of Roma, AC Milan and Spartak Moscow having seemingly failed to materialise, Lyon have emerged as the leading contenders for Depay's signature and head coach Bruno Genesio recently confirmed that the 25-year-old's signature had become a key priority as he seeks to compensate for the loss of Algeria's Rachid Ghezzal.
"Things are progressing," he told the club's official website. "We keep on working. It takes time, discussions ... because recruiting a player now is not easy. I trust the president to get things done quickly. I have put a priority on Memphis Depay. He is a powerful player who scores goals and is good at set-pieces. Rachid has left for the Africa Nations Cup and Memphis knows how to play out wide.
"He is a young player with great international experience and a lot of potential. This is my number one priority. I'm a fan of this player, he has an interesting profile for us, especially as we risk losing Rachid at the end of the season. But there are several things to consider, including the price."
Two players have already exited United during the current transfer window. Third-choice goalkeeper Sam Johnstone joined Aston Villa on loan following Joel Pereira's recall from Belenenses, while midfielder Morgan Schneiderlin completed his move to Everton on 12 January for an initial £20m fee that is expected to rise to £24m.