However, despite the ongoing financial uncertainty behind the scenes and no guarantees Grant will be able to strengthen the squad during this January transfer window, the Israeli coach is determined to enjoy the encounter with the 1987 winners.
"I watched many, many FA Cups, especially finals," said the former Chelsea boss.
"The first I think when I was 18, Leeds against Sunderland, 1-0 to Sunderland, [Jim] Montgomery was the goalkeeper.
"The cup is a one-off game, and in one game, anything can happen.
"If in the league Portsmouth beats Liverpool, Liverpool can still be in the top four - but if we do it in the cup they are out.
"This is what's special about the FA Cup - one game can change everything."
Grant, though, accepts it is down to his team - set to be without on-loan Tottenham midfielder Jamie O'Hara as well as four players at the African Nations Cup - to get themselves out of their current predicament.
"At the end of the day we need to come to the pitch and we need to do our job," he said.
"Even with the [financial] problems we need to do our jobs, we are thinking about football and how to win the games, even if it is not easy."
Grant is not expecting an easy ride against the Championship side, managed by former Fulham boss Chris Coleman.
"Our scouts have watched them and said they are a difficult team," confirmed Grant.
"You know in the FA Cup, that teams who come from the Championship or other leagues give 150% which is understandable, but still we want to succeed in this game.
"I don't think there is a game which will come whether there are problems or no problems that we don't want to win."
Defender Steve Finnan has called for Pompey not to dwell on their latest defeat, when they were out-played by the title-chasing Gunners, who ended up comfortable winners.
"Overall, it is one to forget," he said.
"We have got the FA Cup game next and some very big games to come after that so hopefully we can get over this - we will have to."
Finnan added: "It is frustrating that we have not been able to kick on after the Liverpool result, but we are still four points behind [safety] and after losing the first seven games of the season, we would probably have taken this position.
"There is still a long way to go and there are plenty of games where we can get points."
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