No Asian player has scored 1000 goals as yet.
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1281 However he only has 667 official goals. 614 of them are in friendly and charity games.
Romario and Pele of Brazil hold this record.
In terms of official matches, i think it is Josef Bican, a Czech-Austrian striker. He scored 804 goals (this is a lower bound so the actual number may be higher). If you include unofficial matches (friendlies, army etc), he scored more than 1467 goals - 6 more than Germany's Gerd Muller who bagged 1461 (735 official) goals.Also notable is Pele, who scored 1284 goals (765 official)how ever liverpools steven Gerrard has scored 5000 goals in 1 game
The goal was actually goal number 1000 , and it was scored by Les Ferdinand.
Because the question has a lot of holes, most field goals or touchdowns. Now because you used said "player scored the most" we will start with field goals. Morton Anderson has field goals in his career with 5 teams (6 but was with Atlanta twice). Now to most TD's - Jerry Rice leads with 208 career touchdowns playing with 3 teams. http:/www.nfl.com/history/randf/records/indiv/touchdowns