All we can do is go by the stats and at the ripe old age of 27 (soon to be 28 next month) is unlikely to dramatically improve but could be a late bloomer like Vardy, fingers crossed. Let's have a look at his most recent few years statistically:
12/13 season
Played for Karpaty Lviv in Ukrainian Premier league - 17 games, 8 goals, 3 assists.
Played mainly as a winger (right more) and mainly not in the squad due to his 17 games played
13/14 season
Played for PAOK Thessaloniki in the Greek Premier league - 31 games, 9 goals, 11 assists.
Played mainly as a right winger and to a much lesser extent, an attacking midfielder.
14/15 season
Played for Deportivo de La Coruña in La Liga - 22 games, 6 goals, 3 assists.
Played mainly as an attacking midfielder and to a lesser extent secondary striker. He missed 9 games due to not being in the squad and 6 games due to injury.
15/16 season (latest)
Played for Deportivo de La Coruña in La Liga - 36 games, 17 goals, 10 assists.
Played mainly as a CF (28 games - 11 goals) and to a lesser extent SS (9 games - 8 goals)
He certainly is making an improvement year by year and has played all along the front three as well as advanced midfielding positions, which indicates that he is multi-skilled and can pass and move with it from deep. What is heartening to see is that his latest role has been primarily a striking one and he has scored a decent amount as well as assisting. However, it is unlikely that he will be a goal machine and other notable players around him such as Sanchez, Ozil, Ramsey, Cazorla etc will have to contribute significantly more if Perez is to be our main striker. Only way we stand a chance of challenging is if goals are contributed across the board.