Arshavin have recently been linked with a move to Juventus, after failing to find his best form again in North London.
“We have had no contact,” Wenger said.
“As soon as a player doesn’t play fantastically well, he is criticised. We all know that. I am very happy with Arshavin.
“I believe he is a great player – he is going through a period where it is more difficult for him at the moment.
“But he works very hard in training – his attitude is fantastic and I am desperate to keep him.
“He played almost every single game since the start of the season and has played for his national team as well. Physically he is a bit less fresh.
“After a breather of a few games he will come back stronger than ever because he works very hard in training.
“As far as I know, I believe he and his wife are happy in London, but what is very important as well is that I am very happy with him.”
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.