Dosti began his career with Teuta Durrës, making his debut at the age of 17. He has played over 6 league games for the club since making his debut in the 2007–08 season.
Kukësi
On 23 August 2013, Dosti joined fellow top flight side Kukësi by penning a 1+1 contract.[1]
Montana
On 16 July 2015, Dosti signed a two-year deal with the Bulgarian side Montana, a club which plays in the elite of Bulgarian football.[2] On 3 August, he made his A Group debut from the bench, coming into the game for Ivan Minchev in the 77th minute during the 2–1 loss against Litex Lovech at Lovech Stadium.[3]
Laçi
On 27 January 2016, Dosti returned in Albania by signing a six-month contract with Laçi of Albanian Superliga, rejoining his first manager Stavri Nica.[4]
Šibenik
On 12 July 2016, Dosti completed a transfer to Croatian Second Football League side Šibenik, penning a one-year contract.[5] During an interview, he said that he turned down several offers from Albanian clubs just to play in Croatia, where, according to him, is shown proper attention to players.[5]
Teuta Durrës
On 4 July 2017, Dosti returned to his first senior club Teuta Durrës by signing a contract for the 2017–18 season with an option to renew, taking the squad number 10.[6] This marked his return in Durrës after four years, and Dosti commented this by stating: "I'm very happy to be part of Teuta for the upcoming season. I promise that I'll extenuate that trust of Teuta directors on me."[7] Dosti started the season on 9 September by playing full-90 minutes in the opening match of 2017–18 Albanian Superliga against Luftëtari Gjirokastër which was won 2–1 at home.[8] His first score-sheet contributions came later on matchday 5, scoring his team's only goal in a 2–1 home loss to Partizani Tirana.[9] On 30 October, following the 2–1 defeat at Lushnja which was the fourth consecutive and fifth in six matches,[10] Dosti was released by the club due to bad performances and being tagged as one of culprits for the team crisis.[11]
Kukësi return
In November 2017, following his release from Teuta, Dosti returned to Kukësi but only to train and is set to sign in January transfer window.[12]
SV Bevern
In December 2017, Dosti signed for German club SV Bevern.[13]
^"Литекс - Монтана 2:1, мачът по минути" [Litex - Montana 2:1 match in minutes] (in Bulgarian). Lovech, Bulgaria: blitz.bg. 3 August 2015. Retrieved 11 September 2015.
^Drilon Xhepollari (4 July 2017). "Albi Dosti afrimi i radhës te Teuta" [Albi Dosti the next approach at Teuta] (in Albanian). Telesport.al. Retrieved 8 November 2017.
^Andi Deçka (9 September 2017). "Teuta e nis me fitore, thyen 2–1 Luftëtarin" [Teuta starts with a win, breaks Lufëtari 2–1] (in Albanian). SuperSport Albania. Archived from the original on 10 September 2017. Retrieved 9 September 2017.