Thellufsen was promoted to the senior team of AaB along with U19 teammates Magnus Christensen, Morten Rokkedal, Sebastian Grønning, Joakim Mæhle and Bardhec Bytyqi during the 2016–17 pre-season.
Sports Director of AaB, Allan Gaarde, described Rasmus as a classic creative midfielder with forces in dribbling and creating the unexpected.
[3] The 28 of August, Thellufsen debuted in the Danish Superliga as a substitute for an injured Kasper Risgård in the 34th minute against AGF.
[8] On 25 July 2021, Thellufsen scored his first goal for Lyngby, securing a 2–1 away win over Nykøbing deep into injury time, after having come on as a substitute for Magnus Westergaard in the 81st minute.
[13] In January 2024, Thellufsen returned to Denmark, signing with Danish 1st Division side Vendsyssel FF.