The Aussie defender admits that he, Tony Hibbert and Johnny Heitinga have a friendly rivalry for the club's right-back slot.
But after getting the nod at Old Trafford at the weekend, Neill admits he is desperate to keep his place for the Blues' two massive matches this week.
Everton go to Hull tomorrow night aiming to erase the memory of Saturday's disappointing display at Manchester United, then face neighbours Liverpool in the Merseyside derby on Sunday.
'It's always nice to play,' explained Neill. 'I've just to keep working in training and when you get the chance to play you've got to try and put a good workload in.
'It's not up to me to decide if I've done enough to stay in for the next game but I hope I've put something in the manager's mind to keep getting picked.
'It's a friendly rivalry (for the place) and kind of good for the manager because he's got the choice of various players to play in the positions.
'Of course he doesn't have Johnny and I for European games, that's something which will come in January when hopefully we'll be knocking on the door for places in Europe and the League.'
Despite one of the worst injury crises in recent years at Goodison, the one area of the side where David Moyes has had options in recent weeks has been at right-back.
Lucas Neill, who was left out at West Ham, was back in the side at Old Trafford on Saturday, but Tony Hibbert came on late in the match as Neill pushed further forward while Phil Neville, who can also play at full-back, is making steady progress from his knee injury.