Born in Naples, Verde is a youth product from Roma. Verde featured for the A.S. Roma Primavera side that qualified for the knockout stage of the 2014–15 UEFA Youth League, finishing 2nd in their group, Verde scoring twice in the group stage, both coming in wins against CSKA Moscow. Verde made his senior debut on 17 January 2015 in the Serie A fixture against Palermo, replacing Juan Iturbe after 75 minutes of a 1–1 away draw. On 8 February 2015 Verde starred on his first start for Roma, playing 90 minutes as they won 2–1 away at Cagliari, with Verde assisting both of Roma's goals, for Adem Ljajić and Leandro Paredes. On 9 July 2015 he was officially transferred on loan to Frosinone. On 6 January 2016 he was transferred on loan to Serie B sidePescara for the remainder of the 2015–16 season. On 15 July, fellow Serie B side Avellino confirmed that Verde had joined on loan from Roma. Verde played from start to finish in Avellino's 2–0 away defeat against Bassano Virtus in round one of the 2016–17 edition of the Coppa Italia on 7 August. On 8 August 2018, Verde joined to Spanish La Liga club Real Valladolid on loan until 30 June 2019 with an option to buy.
On 16 July 2019, AEK Athens agreed with Roma for the transfer of the young winger to the Greek club for an estimated transfer fee of €1 million, plus a resale rate of 30%. Verde will sign a three-year contract, earning €750,000 per year and will be given the number 7 shirt, upon request. The following day, AEK officially announced the acquisition of the Italian winger. On 7 December 2019, he scored his maiden goal for the Athens-based club with a stunning free kick which beat Jérémy Malherbe with the help of the right post, in a hammering 5–0 home win game against Panionios. On 5 January 2020, Daniel Verde came on after the restart and gave a new wind to the home side, and he deservedly added his name to the scoresheet with AEK's second penalty of the game with eight minutes remaining, sealing a 3–1 home win game against Panetolikos. On 23 February 2020, Verde scored a brace with clinical side-footed finish, as a resurgent AEK Athens continued their impressive form with a convincing 3–0 home win over OFI. On 14 June 2020, he came in as a substitute and scored with an excellent left-footed strike, sealing a 2-0 away win against OFI. On 12 July 2020, he converted a penalty in a 3-1 away win against Panathinaikos.
