The Owls left-back – on a season-long loan from Premier League side Watford – is keen to make his move to Yorkshire a permanent one.
The 30-year-old is the No 1 choice at left-back and Watford and Wednesday are understood to have held talks last month, without agreeing a deal.
With Pudil still having 18 months left on his contract at Vicarage Road, the Hornets want a fee for the Czech Republic international.
So, having seen fellow loan players like Jack Hunt and Gary Hooper secure permanent Owls deals in January – as head coach Carlos Carvalhal looks to tie down the futures of his promising team – Pudil has had to stay patient and concentrate on his football.
“I would like to stay here and that’s why I am doing everything can at the club to make the supporters proud,” said Pudil.
“It’s not a question for me, maybe you need to ask someone else. I don’t know how close the two clubs were (to agreeing a deal).
“It’s not my part of the job. My job is to play well, I have an agent and he’s talking to Wednesday and Watford. I think they are still talking, trying to find a solution to keep me here.
“I don’t want to move anywhere else, I have settled down with my family here.
“I have two children, one is in school and the daughter is four months old. We would really like to stay here. We will see how things go after the season ends.”
It could be a busy summer, with Pudil likely to be involved in Euro 2016 with the Czech national side.
It is a burning ambition of the defender’s to play in a major tournament, like the European Championships.
The former Slavia Prague and Genk defender said: “Next month we play Scotland and Sweden (in friendlies). I am putting everything into playing for Wednesday, so, hopefully, I will be in the squad for those two games.
“Probably, if I am in that squad, then there’s a big chance I will be involved at Euro 2016.
“I am looking forward to that, because I missed two Euros in years before, so I want to be there for the first time in my life.
“Since I started playing football I have achieved so many things. I won the league championship in Belgium, played in the Champions League and for my country. The other one is to be in the Euros, and that is a big task for me.
“You cannot stop the years, I am getting older, 30 now, and maybe this is my last chance to be at the Euros and achieve something with the Czech team.
“First of all, though, I want to give everything for Sheffield Wednesday, that’s important.”
Pudil has yet to taste defeat at Hillsborough as an Owls player, having not played in the only home loss of the season, to Middlesbrough back in August.
The Owls host Brentford today sitting sixth in the Championship, and Pudil believes one of Wednesday’s strengths this season has been their depth of squad.
That was highlighted in last week’s trip to Birmingham City, when Wednesday lost three players from their starting line-up within 15 minutes of kick-off, yet still won the game.
Midfielder Kieran Lee pulled out of the pre-match warm-up, goalkeeper Keiren Westwood was stretchered off with a neck injury, and Sam Hutchinson limped off with knee trouble.
But Wednesday had strength in reserve in Wales international stopper Lewis Price, Lewis McGugan and Atdhe Nuhiu to come off the bench.
“I came after six games when the season had already started, and the team was building,” said Pudil. “Now you can see we have a big squad, more than 30 players, and everyone can play.
“You need a big squad to achieve something, and we are doing well because of that. Everyone can be ready for the game, step onto the pitch and do well for the team.
“Against Birmingham, it was a difficult first 15 minutes. Even before the game, Lee got injured, then Westwood and Hutchinson, so we had to make three changes.
“I think everyone who stepped onto the pitch did well, and that’s why we won the game.
“When we went 1-0 down, we were still pushing and we showed our character.”
Now the Owls are in the play-offs, they must learn to contend with raised expectations from supporters. But Pudil insists nobody is getting carried away in the surge of optimism which currently engulfs S6.
He said: “I don’t think anyone expected this, to be where we are, and the supporters are really happy. The expectation from them is a little bit high now, but we have to be focussed and keep our feet on the floor.
“We have 16 games to go, and it’s still too far away to predict anything. Of course, everyone would love to achieve something at this club – Sheffield Wednesday are one of the biggest clubs in the world – and the supporters and the club deserve to be in the Premier League.
“No-one is talking about this right now, because it’s far away, and a lot of teams are looking at the Premier League.”
Aiden McGeady made his full debut at Birmingham, and the on-loan Everton winger will need game-time to build up his fitness.
But head coach Carvalhal believes the 29-year-old Republic of Ireland international is a player who will excite Owls fans.
“It was the first game he had played in in a long time,” said Carvalhal. “I talked with him. In some moments, he showed how he can help the team. I’m sure, with time, he will be an exciting player for our fans.
“I can’t say whether it will take him one, two or three weeks to get up to speed but he is showing signs that he’s adapting.
“He’s a fantastic player with good ability.
“It will take him some time to learn the way we play but he is learning very, very fast.”