Allardyce recently admitted a desire to strengthen his strikeforce, with Dindane one of a number of options, but high on the list after failing to sign him in the January transfer window.
The Ivory Coast forward now finds himself in limbo as one further appearance for Pompey will activate a clause whereby they must sign him permanently, which they cannot do given their financial crisis.
"We almost signed him on transfer deadline day, but was a little too late," said Allardyce.
"But he's played in the Premier League which is a good indication he can play at that level, and he's scored a few goals.
"All in all we would be interested depending on what the financial situation is."
Meanwhile, Allardyce has defended Martin Olsson against the barrage of criticism faced by the young star this week.
Olsson has been roundly condemned for apparently claiming he dived to win the penalty that enabled Blackburn to beat Burnley in their local derby on Sunday.
The 21-year-old is reported to have said he "took a chance" when he noticed the outstretched leg of goalkeeper Brian Jenson, and that he "maybe.overplayed my fall a little bit".
Allardyce insists the Swedish winger's comments have been twisted, but despite that, has still been forced to take internal action to underline the fact he does not condone such behaviour.
"I'm not sure, first and foremost, that Martin said what he did, but unfortunately for him and us, he's been criticised unfairly," said Allardyce.
"We all know he has gone down easily, anticipating a challenge that was going to come.
"From where I was sat in the directors' box there was no doubt at all in my mind it was a penalty.
"From Mike Dean's position there was no doubt as well, but we can see from other angles after the game that it wasn't.
"In fairness, the times we've been hard done by outweighs 10-fold the fact we got this one in our favour."
In contrast, Allardyce feels barely a mention will be made of the dubious penalty won by Cesc Fabregas last night that earned Arsenal a draw in the first leg of their Champions League quarter-final with Barcelona.
"If that wasn't a dive either, then what was?" added Allardyce.
"I'm sure there won't be the same fuss about that as there was about Martin, who has been slaughtered by every man and his dog."
Even if Olsson's comments have been misinterpreted, Allardyce has had to act, and will do so again no matter the circumstances or the situation.
"I don't condone it, of course not," insisted Allardyce.
"We've dealt with it internally, talked about it and gone through our code of conduct to say it wasn't right.
"I've spoken to Martin about it, he's accepted it, and we move on."