The midfielder’s one-month spell ends after tomorrow’s trip to Coventry.
Yet the Scot has told Guy Whittingham he is eager to remain at Fratton Park.
That has delighted the Blues’ caretaker boss, who also wants Allan to stay.
Now Whittingham will broach the issue of an extension with Allan’s parent club West Brom.
Despite the emergency loan window ending yesterday, clubs are allowed to renew existing loans.
And Pompey are seeking for Allan to stay up until January.
Whittingham said: ‘Of Scott’s initial loan period, tomorrow is his last game.
‘But if all parties are agreed, we will be extending it.
‘He would like to stay and we would like him to stay. We are just looking for confirmation that West Brom feel the same way.
‘All being good, that will happen.
‘If he goes back to West Brom, he can’t go anywhere else until January. If he stays here he plays games.
‘We need players of ability. There are obviously going to be games when you are looking to use him – and on occasions when you think this isn’t the match for him.
‘That’s the issue with Scott. He gives you a lot on the ball but needs to work hard defensively off it.
‘We know that, West Brom know that.
‘He is one of those who will score you the odd goal, but can also provide that telling pass for us.’
Allan has so far made three appearances since rejoining Pompey on loan on October 29.
However, he was forced to sit out three matches through suspension following his sending off in the FA Cup defeat against Notts County at the start of this month.