Rice considering England switch - Ireland boss O'Neill
The West Ham teenager has started three friendlies for Ireland, making his debut in March, but is able to change allegiance as he has not yet played a competitive fixture.
Rice has not been named in O'Neill's preliminary squad for Ireland's meeting with Wales in the Nations League on September 6.
And O'Neill fears the 19-year-old, who can play in either defence or midfield, may make the switch to England.
"He is still deliberating. He is a young man," O'Neill said.
"England have spoken to him. He is taking time to make his mind up. He has done brilliantly for us. I'm giving him a little bit of time.
"I wouldn't be exaggerating to say Declan has loved it with us. After the Turkey game [Rice's senior Ireland debut] his father was there and it was a joyous moment for them.
"We have done everything we can. He has been welcomed by the squad, the fans. He is taking time and I am respecting that."
O'Neill: I wouldn't be exaggerating to say Declan has loved it with us. After the Turkey game his father was there and it was a joyous moment for them. We have done everything we can. He has been welcomed by the squad, the fans. He is taking time and I am respecting that. #COYBIG
— FAIreland (@FAIreland) August 27, 2018
Rice's situation mirrors that of Aston Villa winger Jack Grealish, who represented Ireland at youth level before declaring for England in 2015.
The 22-year-old, linked with a move to Tottenham in the transfer window, has played for England's Under-21 side but is yet to feature for the senior team.
His only start in the Premier League this season came in West Ham's opening 4-0 defeat at Liverpool, where he was substituted at half-time.