The 24-year-old played the final match of his season-long loan in this afternoon's 4-2 win over relegated Reading at Upton Park, where captain Kevin Nolan netted a hat-trick.
Despite only scoring seven goals, the 6ft 3ins striker proved a popular signing, and this week earned a recall to the England squad for the friendlies against the Republic of Ireland and Brazil.
Yet with Liverpool set to be holding out for £17million and Newcastle and Monaco also said to be monitoring the situation, the Irons are set for some tough dealings.
Allardyce, though, remains determined to land his top target.
"It is our target to make it a permanent situation," he said. "Hopefully we can get somewhere in the near future to do that.
"It's our main priority. There are negotiations between the club and Liverpool.
"We have to pursue it to the very end one way or another and we will find out as quick as we can if it is a yes or a no.
"If we can start with Andy Carroll that would be a great achievement for us as he can only get better and better.
"Then we build around that in terms of how we want to improve next year, with better quality.
"Andy is a player that is wanting to enjoy his football. He lives for his football and wants to play every game. He wants to use his strengths and score as many as he can - but he also works very hard for the team."
The Irons were in complete control against Reading today after a mistake from a new England call-up, goalkeeper Alex McCarthy, gifted Nolan the opener on 23 minutes, with Ricardo Vaz Te sweeping home a second following more good work from Carroll.
The Royals responded with two quick goals at the start of the second half through Garath McCleary and substitute Adam Le Fondre.
The Irons, though, made sure of a creditable top-10 finish when Nolan netted again and then completed his hat-trick with a header three minutes from time.
Allardyce said of Nolan: "He has always been top class. It's another double-figures scoring job he's done yet again. He's done many of those throughout his career and finishing the season with a hat-trick has got to be thrilling for him."
"When we needed Kevin again he was there. That's what he is good at. When he scores his goals they are always very important."
Reading's fate had long been sealed and they finish the season in 19th place.
However Royals boss Nigel Adkins maintains there are plenty of positives to take ahead of a return to life in the npower Championship.
"There is a good feelgood factor going forward for next season, which is important," said Adkins, who replaced the sacked Brian McDermott in March.
"We have changed the way the club has played football - we are looking to be more in control with keeping the football for longer periods of time and that takes time to get everyone ready to go and do that."
Adkins felt his side had given a good account of themselves on the final day of the season.
"Great credit to the players, they showed really good character and in the second half we came out and scored two good goals. We were in the ascendancy up until they scored the third," he said.
"That was a shame but it's what you do in both penalty areas."
Adkins - a former goalkeeper himself - also had words of comfort for McCarthy as the 23-year-old prepares to link up with the senior England squad for the first time.
He said: "Alex is still a young goalkeeper. It's all a good learning experience. He just needed to clear the football, didn't he? It was a poor execution and that's life.
"The big thing I've noticed with Alex is if he does make a mistake he can quickly forget it, which is important in a goalkeeper.
"It's how quickly you can move on and Alex has done that.
"He is going to develop into a really good goalkeeper."