Asked if Mata's father had been invited as a guest of Arsenal, Wenger said: "No. I don't know. Maybe."
Arsenal's main immediate targets are at Real Madrid, with the club interested in Ángel di María, Mesut Özil and Karim Benzema. Although Benzema is unlikely to move, Di María and Özil are expected to be made available if Madrid do seal their world record transfer of Gareth Bale.
With Alex Oxlade-Chamberlain and Mikel Arteta both out, Arsenal are especially keen to enhance their midfield and attacking options.
"We paid a heavy price on the injury front as we lost Podolski," said Wenger. "I don't know how bad Ramsey is, I don't know how Wilshere responds to an ankle problem. Podolski is definitely out for 21 days. The tackles on Wilshere were disappointing."
Despite having already used his three substitutes, Wenger urged Wilshere to come off after a challenge on 82 minutes by Raul Meireles. He also told Ramsey to join him on the bench during injury time rather than further risk his groin.
Wilshere, though, insisted that he wanted to stay on. "I would have played with 10 men," said Wenger. "We were 2-0 up and they had to score five goals in 10 minutes. Even with 10 men we could have avoided that. Jack should be all right for Sunday and I am hopeful on Aaron as well."
Asked if the injuries would force his hand in the transfer market, Wenger said: "Yes. I cannot tell you more than that we are in the market. The whole world knows that now."
As well as the three Real Madrid players, Wenger retains an interest in Newcastle's Yohan Cabaye and will almost certainly add Mathieu Flamini on a free transfer.
Alan Pardew, the Newcastle manager, said yesterday that Cabaye had only a 50-50 chance of securing his desired move. Arsenal have still not improved the £10.2 million bid that was rejected last week, with Newcastle valuing Cabaye at £20 million.