Mühren was born in Purmerend. He made his professional debut for boyhood club FC Volendam on 5 August 2011, playing the full ninety minutes in an Eerste Divisie match against FC Dordrecht; the game ended 0–0. His first goals for the club came in an Eerste Divisie match on 30 September, netting twice in the first half as Volendam defeated Fortuna Sittard 3–2. On 10 February 2013, Mühren netted his first professional hat-trick, and fellow strike-partner Jack Tuyp also scored a hat-trick as Volendam defeated Telstar 6–2.
2013–14
On the opening day of the 2013–14 Eerste Divisie season on 3 August 2013, Mühren scored all of Volendam's goals in a 3–2 away victory over Almere City. In a KNVB Cup match against Eredivisie heavyweights Ajax on 25 September 2013, Mühren netted a brace as Volendam fell to a 4–2 defeat in extra time. The game came just six daysafter the death of Robert's uncle Gerrie Mühren, who started his career with Volendam before going on to be a part of the great Ajax teams of the 1970s that won three consecutive European Cups. On 10 February 2014, Mühren netted twice in the first half before completing his hat-trick in the second half, as Volendam defeated Jong FC Twente 4–2. In the 32nd round of the Eerste Divisie tournament on 21 March, he scored in either half as Volendam defeated Jong PSV by a score of 3–1 at the Kras Stadion. By scoring in Volendam's next fixture, a 2–1 defeat to Excelsior on 28 March, Mühren reached 24 league goals for the season and had completed a remarkable run of scoring in eight of his previous ten appearances.
AZ
On 28 August 2014, Mühren signed a three-year deal with AZ Alkmaar, leaving for a fee of 350.000 euros. After three years at AZ, some of which spent with the reserve team, the midfielder moved to Jupiler Pro League side Zulte Waregem.
He scored on his debut in The Netherlands' top division, in a 1–1 draw at home to PEC Zwolle. Muhren finished the season as Sparta's top scorer, but the side were relegated via the play offs at the end of the season.
Personal life
Mühren is the nephew of former Dutch internationals Gerrie Mühren and Arnold Mühren. Arnold played for Ipswich Town in the 1981 UEFA Cup final, beating Robert's former club, AZ.
