The Northern Irishman has signed one player as Celtic boss.
The Northern Irishman has only signed one player - highly-rated French sensation Moussa Dembele, for £500,000 - this summer after replacing Ronny Deila as Hoops boss.
But speculation remains rife about Liverpool right-back John Flanagan and Blackburn Rovers centre-half Shane Duffy - the latter of whom could be the subject of a bid by Rodgers this week, according to The Glasgow Evening Times.
With Old Firm rivals Rangers signing eight players this summer, it will look poor for Rodgers come next May if Celtic fail to win a sixth successive Scottish Premiership title.
That failure would be traced back to what did or did not happen during the summer transfer window, but the former Liverpool boss says that he might more information about arrivals in the coming days.
“There is a couple of players that we are looking at but we will see how that develops over the coming days," he said via The Sunday Post.
Celtic host Lincoln Red Imps at Parkhead tomorrow as Rodgers's side look to overturn a humiliating 1-0 first-leg deficit by the semi-professional Gibraltar side to reach the third qualification round of the Champions League.