The 31-year-old has signed an 18-month contract at Upton Park to end a miserable spell at Anfield.
Cole won the last of his 56 caps in the World Cup defeat to Germany in South Africa but Allardyce believes should the midfielder rediscover his top form with the Hammers then he would start to attract interest from Roy Hodgson as he prepares for the 2014 World Cup in Brazil.
"There is still an awful lot of football left in him, and Joe feels he needed a break somewhere and recreate himself," said Allardyce at Friday's press conference ahead of the FA Cup third-round tie against Manchester United.
"We have the backup staff behind the scenes here to help him do that.
"Extra quality in a team is always important and we know Joe's strength lies in possession and being able to open teams up and that is what we will be saying to him, to go and create some goals for us."
Allardyce continued: "If he can recapture his old form and plays on a regular basis for us Joe is bound to get a bit of interest from Roy coming around to the next squad.
"But his main focus will be making sure he plays for West Ham on a regular basis and producing the form we know he can."
Cole emerged from West Ham's academy to sign professional terms in 1998 and helped them win the FA Youth Cup the following year, becoming a firm fans' favourite before leaving for Chelsea in 2003, when he became one of their first signings following Roman Abramovich's takeover of the club.
There, he won eight major trophies including three Premier League titles and was named in the Professional Footballers' Association team of the year in 2006.
But after joining Liverpool as a free agent in 2010, he was sent off on his Premier League debut and missed a penalty in his next appearance, a Europa League qualifying match against Trabzonspor.
The poor start set the tone for a Reds career hampered by form and fitness problems and he was allowed to spend last season on loan at Lille.
He scored nine goals in 42 appearances for the French club and will now have the opportunity to further rebuild his career at the club where he first made his name.
"Joe is coming home, he realised his ambitions here as a footballer," Allardyce said.
"It is a pleasure to bring him back, to try to give him the sort of football opportunities he is looking for.
"We will give him that and hopefully he will grasp it with both hands and produce some of the outstanding quality which we know he has.
"If we can extract the best out of him again, then it will be an outstanding signing for us."
West Ham will have captain Kevin Nolan and defender James Collins back from suspension on Saturday after they missed the 2-1 Premier League win over Norwich on New Year's Day.
The Irons, however, still have several men sidelined, including England striker Andy Carroll while full-back Joey O'Brien faces a fitness test on his hamstring.
United are expected to make several changes for the late afternoon kick-off, but Allardyce does not expect that to weaken the Premier League leaders at all.
He said: "We are not under the same pressure as we are under in the Premier League that is for sure, but we have a responsibility because there will be a full house at West Ham on Saturday, live on TV so we have to put the best team out we have available.
"We are suffering from a few injuries, so are grateful we will have our suspended players back which helps us.
"I am sure Sir Alex will make some changes, but it will not really make much of a difference because at the moment any changes he does make, they still keep winning.
"They are in top form, so it will be hugely difficult, but a fantastic one to be involved in and if we can create a bit of an upset it would be a great bonus to make it into the next round."