Andreev made his debut at ATP level at the age of 15, when he received a wild card for the qualifications of the 2016 Moselle Open, where he lost to Michael Berrer. Andreev played at the 2017 Sofia Open in his homeland, losing in two sets to Maximilian Marterer in the qualifications. Next year, Andreev received another wild card, this time for the main draw of the 2018 Sofia Open event, but lost to Denis Istomin. The 17-year old Bulgarian became the first player born in 2001 to play in the main draw of the ATP World Tour. In the 2019 Sofia Open, Andreev was granted another wild card for the main draw. The Bulgarian pushed world No. 45 Matthew Ebden to three sets, but ultimately lost in the third set tie-break. A year later Andreev received another wild card for the main draw at the 2020 Sofia Open, but couldn't go past John Millman.