Spurs refused permission for the 23-year-old to play in Pompey's FA Cup game with Coventry on Saturday and with the south coast club's financial problems there had been reports O'Hara could return to White Hart Lane.
However, with Pompey waiting to see whether their transfer embargo will be lifted when the Premier League television money is paid on January 10 there is still a chance O'Hara will stay, much to the delight of Grant.
"I want to keep Jamie. I spoke with Harry Redknapp and he said that it's OK and I hope it will be," said the former Chelsea boss.
O'Hara's loan could pave the way for David James to leave Fratton Park with reports on Sunday indicating Tottenham are poised to make a move for the England international in the January transfer window.