Mata's father and agent, also called Juan, was reportedly in attendance at the Emirates Stadium on Tuesday, when Arsenal beat Fenerbahce 2-0 to complete a 5-0 aggregate win in their Champions League play-off tie.
Mata was an unused substitute in Chelsea's 0-0 draw at Manchester United on Monday, sparking media speculation about his status at Stamford Bridge, and Wenger admitted he was a fan of the Spain international.
"I've heard like you, because I watched the game last night (Monday), that Juan Mata could be on the market," Wenger told journalists.
"I don't know. There is always a reluctance in England to sell to each other. Yes, I like him."
However, when asked if Mata's father had attended the game against Fenerbahce as a guest of the club, Wenger replied in enigmatic fashion, saying: "No. I don't know. Maybe."
He was even less willing to discuss a possible bid for United striker Wayne Rooney, with whom Arsenal were linked earlier in the transfer window.
"We cannot speak about players who are under contract with other clubs," Wenger said.
"Because when a player is under contract in another club, he has to respect the contract. So if you want to buy the player, you have to speak to the club first."
Many of Arsenal's fans are desperate for Wenger to invest in new players, after mooted moves for Rooney, Liverpool striker Luis Suarez and new Napoli signing Gonzalo Higuain failed to materialise.
Arsenal's apparent need for new blood was exacerbated on Tuesday when Lukas Podolski had to go off against Fenerbahce with a hamstring injury, while Aaron Ramsey and Jack Wilshere also sustained knocks.
"We have to see how bad the injuries are," said Wenger, whose side tackle derby rivals Tottenham Hotspur on Sunday.
"I cannot tell you more than that we are on the market. Everybody knows, the whole world knows that now."
Before leaving the pitch with a groin problem in injury time, Ramsey produced another impressive performance against Fenerbahce, scoring both goals.
He had previously been named man of the match in both the first leg and last weekend's 3-1 win at Fulham, and Wenger is thrilled by the progress of a player whose five years in north London have been blighted by injuries and inconsistent form.
"He gets to the end of things now," Wenger said of the Welsh midfielder.
"I liked especially his second goal. It's a good finish. A year ago he wouldn't have taken that chance the way he took it tonight.
"He's improving from week to week. That's very positive because a year ago, many people were questioning Aaron Ramsey."
The success against Fenerbahce took Arsenal into the group stage of the Champions League for the 16th season in succession – a feat matched by only United and Real Madrid.
Although the club's trophy drought is set to stretch to nine years this season, Wenger feels it is an achievement worthy of acclaim.
"I believe that at the top level, the most difficult is to be consistent," he said.
"Of course it's an achievement, because if you look at the clubs in Europe, only three clubs have done it in the whole of Europe.
"I hear a lot that it's not enough and I agree with that, but still it shows we've been remarkably consistent. But our ambition is much higher than that."