"It is a big achievement to sign for a big club like Arsenal so I'm just delighted with the contract and hopeful that I can sign it soon," Nelson told British media.
"I did set one target - to make my first-team debut. I have done that, I have had 15 appearances.
"A Premier League start was on the cards but I think I need to score, that is the only one I haven't achieved so fingers crossed I can get a cheeky goal before the end of the season."
Nelson has benefited from Wenger's decision to rest key players against Southampton, making seven changes from the side who beat CSKA Moscow 4-1 in the first leg of their Europa League quarter-final.
"He (Wenger) is one of the biggest (influences) for me," Nelson added.
"He keeps pushing the youngsters – me, Eddie Nketiah and Joe Willock – I think he has got a bight future planned for us."
Arsenal visit Moscow for Thursday's second-leg against CSKA.
(Reporting by Hardik Vyas in Bengaluru; Editing by Peter Rutherford)
