The relegated Hammers are already looking to strengthen their squad for the Championship as it appears likely that some key players will depart this summer.
But Allardyce has spoken out about West Ham's current stance on transfers, saying nothing is likely to happen in June, effectively quashing rumours that the aforementioned pair may be landing at East London this off-season.
"There has been a lot of speculation about players coming in or leaving the club, but I'm not aware of any bids," Allardyce told the East London Advertiser.
"It's quiet this time of the year because everybody, like myself, is on holiday and things start up again in July. At the moment transfer activity is at a minimum.
" and I don't think we could afford Joe Cole," Allardyce added.