Allardyce has already added six new faces to his squad ahead of the new season but admits the loss of Andy Carroll could tempt him to look abroad one more time before September 1.
Carroll has been ruled out until the end of the year with an ankle injury and Allardyce admits a replacement target man is his priority.
Ecuador striker Enner Valencia and Argentine forward Mauro Zarate have already bolstered his options up front having joined in the summer along with midfielder Diego Poyet, and defensive trio Aaron Cresswell, Carl Jenkinson and Cheikho Kouyate.
"We have gone out and shopped very wisely," said the former Bolton manager. "From my point of view it is about the age of the players as well as the talent of the players.
"The average age of all our signings is 23 years old and I think that's good for now and good for the future. They should be here for a long time, not just a short-term stop-over as some do in their first season or two in the Premier League.
"You look for short-termers to just get you through but now we have moved on to not only improve the squad for now, but also for a number of years to come.
"And they will only get better when they play with us. Our business is done but we are still waiting for another frontline player who can maybe score a few goals.
"That has been very difficult to acquire because of the injury to Andy Carroll but we are still pursuing that avenue as quickly as we possibly can."
Asked if he was optimistic on the chances of adding to his squad with just over two weeks of the transfer window remaining, Allardyce said: "Yes, I think so.
"We will definitely get something done but it is the quality of the player which is the most important thing for me because he has to come here and be available to be used immediately, or certainly in the near future.
"It may not be the case going straight in, there may be a settling period as it's looking more like that player is going to be from abroad now rather from within this country. We are still searching high and wide."