The Spaniard was heavily linked with the managerial vacancy at Liverpool, before the Reds opted for Brendan Rodgers.
And now the Latics boss is one of the early favourites to succeed Harry Redknapp at Tottenham Hotspur.
Scotland international McArthur is confident that Martinez will turn down the overtures of Spurs should they come calling, and insisted nobody is worried about the 38-year-old departing the club this summer.
"As far as I know he is staying, and hopefully that is the case," McArthur said. "He's a brilliant manager and as players we obviously all want him to stay, to continue pushing the club forward and hopefully cracking on into that top 10.
"Obviously with Harry Redknapp leaving Tottenham he'll be linked with that job - and whoever does take over he'll be linked with his old job.
"He'll no doubt be linked with every other job that comes up this summer because of the fantastic work he's doing at Wigan.
"But that's no concern of ours at the moment."
The 24-year-old, who arrived from Hamilton two years ago, added that Martinez has been vital in his development as a player.
"He's been excellent for my career, especially this past year.
"He's given me the chance to step in and play some games, get a run in the side and it's brought my game on no end.
"He's made me become a better player in training as well as matches and I can only thank him for that."
