Sinclair, 21, who has spent time on loan at Wigan, Birmingham, Crystal Palace, Charlton, QPR and Plymouth, is one of three players being targeted.
"We've spoken to Chelsea and we hope to tie something up very soon with Scott," Rodgers told BBC Sport.
"There's one or two things that we're looking at. This is a squad that isn't going to need major surgery as long as I keep the squad I want to keep here and then add just one or two to it.
"One of those is injured but we hope to complete a deal with him, one we hope will be completed in the next 48 hours and one will probably happen before the end of the transfer window.
"All in all, I'm happy with the group that's here."
It appears that Sinclair is the one who will arrive the soonest out of those mentioned, and possibly in time for Saturday's season opener at newly-relegated Hull City.
Trialist Kemy Agustien is the injured player mentioned as Rodgers has previously said he wants to sign the former Dutch Under-21 international.
But Rodgers is confident in the squad he has already going into the first game of the season.
"I've got a great bunch of players," he added. "If we keep the spirit that we have and continue to develop that, and keep hold of the group then you never know where that will take us.
"We are looking to go all guns blazing and look to make a good start.
"Hull is going to be a difficult game. "The opening couple of games are difficult because they are the first competitive ones and you are obviously a bit more tense.
"But this is a league where every game is going to be very close and very tough."
Source: BBC Sport
Source: BBC Sport