Wigan manager Martinez is the bookmakers' favourite to replace David Moyes at Goodison Park, with talks under way with the Merseysiders. Everton chairman Bill Kenwright has stressed the Spaniard is not the only option, but his appointment would be welcomed by some of the club's key players.
"It all sort of seems to be going on at the moment," left-back Baines said. "Thankfully we are in camp so I am keeping it at the back of my mind for now and concentrating more on England. Roberto Martinez has been linked with the job. He is a terrific manager so we will just wait and see."
Everton captain Jagielka, also on duty with Roy Hodgson's side, would also welcome Martinez's arrival, although would be happy with whatever name the club plumps for.
"I will be delighted whoever comes in," he said. "Everton is a massive club and hopefully we can get a fantastic manager."
A decision on Moyes' successor could have well been made by the time the pair return from South America, where England face Brazil in a high-profile friendly at the Maracana on Sunday.
If England are to get a result against the 2014 World Cup hosts, though, they will need to play better than they did against Ireland on Wednesday night.
Hodgson's side were made to look decidedly ordinary by a side 32 places lower down the FIFA rankings, with Frank Lampard's first-half strike earning a draw. However, Jagielka was keen to draw the positives from the game, insisting it will help in their World Cup qualifiers against the likes of Ukraine, Montenegro and Poland.
"I am sure the fans enjoyed the game," the defender said. "It was pretty much end to end. Unfortunately for us we did not manage to get the win, but there are still quite a few positives to take out of it. If you look at the games we have left in the group, especially at Wembley, teams will try to frustrate us.
"After getting the goal, that was Ireland's gameplan - to try and hit us on the counter with longer balls forward. To be fair, they did it well and managed to keep it down to one. We had quite a few opportunities to score a goal or have a killer, final ball, but we will still take positives from the game."
- Sports & Recreation
- David Moyes
- Bill Kenwright
- Roberto Martinez