Wenger also confirmed the club have had no offers for Alexis Sanchez, Mesut Ozil or Jack Wilshere in the current transfer window.
"I tried hard with David Dein [former Arsenal vice chairman] and referees to help them become professional", Wenger said.
As a result, a transfer away from Stamford Bridge could happen this month.
"How do we cope with that?"
Chelsea will look to cement their second place in the Premier League standings, when they face off against London rivals Arsenal at the Emirates Stadium, in their first match of the New Year, on Wednesday night.
Wenger added: "This club has lost many big players and has always responded well".
"Massive players have left this club, so this club will always be in a strong position on that front. But you want to keep your best players, yes".
Referees turned professional in 2001 but despite pushing for the change, Wenger said that they have not improved.
A knee injury has seen Luiz out of action for the Premier League champions since November, but rumours persist that Conte's fall-out with the former Paris Saint-Germain man is also a reason behind his continued absence from the Chelsea squad.
"On the other hand it depends if we manage to extend the contracts of the players who are at the end of their contracts in June. It will depend on that as well, because we will have to take the consequences of these decisions and respond to it". And the Frenchman will be hoping that his side bounce back strongly against the West Londoners on Wednesday. The two who have a little chance are Ozil, who might have a test this morning, but he hasn't been out at all since Crystal Palace, so I don't know.
'At the moment our injury list is quite long, because we lost Kolasinac in the game against West Brom and Koscielny.