Rodallega has been subject to reported interest from the Gunners, with Arsene Wenger keen on recruiting the Colombian star to bolster his frontline.
Villa are also thought to be tracking the 24-year-old, but Martinez says no approach has been made and he is not under pressure to sell the striker.
Rodallega was the Latics' top scorer last term, bagging 10 goals as the club secured Premier League survival, and when asked by Sky Sports News if Wigan had received any offers, the Spaniard said: "No, we haven't."
Martinez went onto to explain chairman Dave Whelan had put him under no obligation to part company with his big players to keep the club's finances in order.
He added: "First of all, we are excited when one our players gets attention from one of the big clubs. It is because the player is enjoying their football and doing well.
"On the other side, we don't need to sell and I think the chairman is quite clear that we are not going to have much money to spend.
"But our strength is that not having to sell to balance the books and that's a great strength in a football club."
The Lancashire outfit have often struggled to keep hold of players attracting interest from rivals club in the Premier League - but Martinez has pledged to keep hold of his key names.
The former Swansea boss rebuffed any overtures for his talisman by suggesting Rodallega - amongst others - would best serve their interests by staying at the DW Stadium.
He added: "We've got a group of young players and we're going to try keep them for a bit longer and allow them to progress.
"We've got players that probably haven't reached their peak yet and they could do that with Wigan Athletic. We'll try to keep everyone to start the season and sign a few players if we can."
While speculation about players exiting the North West may heighten over the close season, Martinez concedes he is unlikely to be bringing players in such are the monetary constraints he is working under.
But the 36-year-old said he still wanted to bolster his ranks as his side look to maintain their stay in the top flight.
When asked if transfer activity would be busy over the summer, Martinez said: "Yes, because we lost a few players.
"We are in a position where we probably need between five and six faces - we already signed two. I think its going to be like any other football club - a little bit late in the window because the World Cup always delays (transfers).
"But I think it's going to be a very busy one, a very exciting one for the fans."