Perhaps there is room for Maxi and Joe Cole in Rodgers' system. But neither put in much of a showing (outside Maxi's knack of scoring braces and hat-tricks months apart) before now. They are 30+ and the high energy game Rodgers plans will not suit them based on that alone, and neither is especially quick out the blocks any more.
Adam loves to either run with the ball or pass it long. Both of these are the opposite of what we want, as we want people to run without the ball and pass it short.
Spearing might do ok, as it's his long passing that generally lets him down, so we can hide that weakness. He's something of a terrier and seems to have the stamina to match.
Downing is our only threat wide on the left (Maxi and Cole will tend to run the channels rather than the touch line). If he plays consistently there he could become a threat for us.
Carroll is basically the only kind of centre forward we need should we choose to play with one. This kind of play suits Suarez as a wide player who cuts in or runs into channels, rather than as a central player who roves around and tries primarily to beat the offside trap ala Torres. (Note that Torres is only ever good for Spain when the opposition is chasing the game and he has more space than he would otherwise get) So if we play 4-3-3, Carroll starts every time, but we have the versatility to play 4-5-1 (including having the options of Suarez or Bellamy up top ahead of Gerrard), 4-4-2 diamond (Maxi/Cole, Gerrard, Aquilani, Lucas behind Suarez and Carroll), or 3-4-3 with Johnson and Enrique pushing up into midfield and Lucas dropping between the CBs. A lot can still be made of this squad if the players are willing to put in the effort.