However, Allardyce has confirmed there is no room in his squad to strengthen and that he is currently forced to adopt a one-out, one-in policy.
It has been speculated Rovers hit-man Jason Roberts could be used as a possible makeweight in a deal to bring Beattie back to Ewood Park.
The former Bolton boss says his squad size is at its maximum and that if he does not offload someone then there will be no fresh faces.
"Unless one leaves, we won't be in for another striker," explained Allardyce.
"We haven't enough room for anybody - be it James or anybody else.
"We're at our limits in terms of squad and financial commitments.
"The older I get, the more I understand this situation. You have to understand the whole business."
Wigan 6/5, Draw 9/4, Blackburn 12/5