The Englishman's comments follow confirmation from Gers owner Dave King that the Ibrox outfit is aiming to raise £6m for summer recruitment in a share issue.
Sutton has warned Rangers that this figure will be nowhere near enough for Gerrard to build a team that can dethrone the Hoops.
"If you've got a share issue why stop at £6m? Why not say more? Why not say £10m, £12m?" Sutton told BT Sport.
"If they're raising £6m, it's not enough. Absolutely not. I think they need £20m, £30m. They need serious investment to compete with Celtic.
"I find that hard to believe. I would be shocked if Steven Gerrard has come up and he has that little in the kitty.
"This is the biggest issue, bar none that Steven Gerrard has. Steven said he would change 13, 14 players yesterday but he can't change that many, absolutely not."