"We have to tackle this problem and not to close our eyes because it is a little bit unreasonable to think that just because we are football we have no problems with it," the Frenchman told Arsenal's website.
The 66-year-old has been approached by the Football Association (FA) to explain comments made to French newspaper L'Equipe following the doping scandal in Russian athletics, suggesting there was a drugs problem in football.
"I am open to talking to the FA, of course,” Wenger said.
"I just mean that you see the doping problem has suddenly turned up in track and field as well. We have a problem in cycling and then (to) think that we in football are immune because they are football players is absolutely wrong.
"I want deeper tests, better tests because what we test is superficial," added Wenger, whose side lost to Dinamo Zagreb in the Champions League in September before a Zagreb player failed a drug test.
"What we want as well is that when people are caught that they are punished and that the clubs are punished as well."
Dinamo midfielder Arijan Ademi is awaiting the results of the analysis of his B sample, taken after the 2-1 victory over Arsenal. His initial test was positive.
Wenger told L'Equipe that he had never had one of his players injected to make them better.
"I've played against many teams that weren't in that frame of mind," he added.
In his latest comments, the Arsenal boss said footballers should be routinely blood-tested rather than submitted to "superficial" urine tests.
"When you play away in the Champions League, most of the time we lose two hours when there is doping control because people cannot fulfil the tests. With a little blood test it takes a minute and you can test much more," Wenger said.
“We sit sometimes on the aeroplane and wait for half an hour, or an hour, until the guys who have the tests can come back and fly back. You come back at 4am because the tests last too long.
"It is simple. Why can we not do it? In every other sport they do it."
(Reporting by Neville Dalton, editing by Alan Baldwin)
