Allardyce has already turned his focus to strengthening his side after they sealed promotion back to the Premier League at the first time of asking beating Blackpool 2-1 at Wembley on Saturday.
The 57-year-old former Bolton, Newcastle and Blackburn manager wants to give his current side a fighting chance of remaining in the top-flight and avoid an immediate return to the Championship next season.
He wants former Upton Park star Cole to spearhead their survival bid and is currently weighing up the possibility of bringing him back to East London once he returns to Liverpool after spending the season on-loan at French club Lille.
The 30-year-old is has impressed during his spell at the Stade-Lille Metropole scoring four times in 32 appearances as the Ligue 1 side secured qualification to the Champions League.
However it’s likely that he’ll be surplus to requirements at Anfield and with the Reds keen to trim their wage bill that could work, financially, in Allardyce’s favour.
He’s also chasing Reo-Coker who is a free agent after activating a release clause in his contract that allowed him to leave Bolton following their relegation.
The 28-year-old former Iron’s captain spent three productive years with the club before departing for Aston Villa in 2007 and then joining to the Trotters last year.
Allardyce’s immediate concern is tying first choice goalkeeper Robert Green to a new contract as the 32-year-old’s current deal runs out at in the summer and has already drawn up a list of potential replacements should opt to leave.
Out-of-contract keepers Manuel Almunia and Craig Gordon and Blackburn’s Paul Robinson are all on his radar whilst Newcastle’s Fraser Forster, currently on-loan at Celtic, is another option although it would cost £1.7 million to prise him away from Tyneside.