"We are here to play against the best teams," he said at a news conference.
"We are not afraid of anyone. We are keen to measure ourselves against the best."
Gunnarsson has been impressed by England's performances so far in France, but is determined to fight for a place in the quarter-finals.
"We have been watching the tournament and I think England have been playing well. They have been playing decent football," he added.
"They didn't score against Slovakia, but they worked hard. We have to do the same. [Monday] is a big game and we are only thinking about that. We have to go out there and fight for it.
"The Austria game was difficult, of course, it was extra sweet to get the win in the end and get the extra two days to recover."