"Ashley is a terrific player but, in the games I've played, I've shown I can come in and do a job as well," said Baines.
"It would be nice to hold onto the shirt if I can. You want to play so, the more games you play, the happier you are. I've started the last few games so I'm very happy with that.
"Do I want more of this? Of course, It's natural. Everyone wants to play so getting the games recently has been nice."
England will next face Poland in Group H on Tuesday.