The 29-year-old midfielder made 30 league appearances for Portsmouth last season, contributing to six goals and scoring two himself.
However, the former Manchester United midfielder has fallen down the pecking order this season, making only three appearances.
Tunnicliffe was the subject of transfer interest in the summer and a move out of Fratton Park is still on the table as the transfer window in Australia is set to close on Saturday.
Cowley admitted that he is hoping that Tunnicliffe will decide against a move away from Portsmouth as they are short of options in midfield with the injuries to Louis Thompson and Tom Lowery.
The Portsmouth boss praised Tunnicliffe for his attitude and professionalism and insisted that the 29-year-old is fighting for the regular first-team spot.
“We hope Ryan will stay because we’ve obviously lost Louis Thompson and also have Tom Lowery injured at the moment”, Cowley told The News.
“It’s an area which we thought was probably our strongest – and unfortunately two injuries later it doesn’t look so strong anymore.
“Will he go? Anything is possible in football, but we hope not.
“I thought his and Kieron’s attitude was good.
“We said at the outset, same attitude, same work ethic and you’ll get the same outcome – and it was proven with five goals.
“They are good professionals, we have high standards, we expect players to be relentless in their work ethic, to be really focused and determined.
“This is a brilliant football club and they are fighting to be a regular in the team.”
Tunnicliffe featured in Tuesday’s third round of this season’s Hampshire Cup clash against local rivals Southampton’s Under-23 side and won the man of the match for his performance.
