The four arrivals so far - Sunderland goalkeeper Simon Mignolet, Manchester City defender Kolo Toure, Celta Vigo forward Iago Aspas and Barcelona B midfielder Luis Alberto - have all strengthened the squad according to Rodgers.
But having missed out on Shakhtar Donetsk midfielder Henrik Mkhitaryan, who joined Borussia Dortmund, the Reds are now turning their attention to other players who can come in and make an instant impact.
That may be increasingly important considering reports are suggesting Arsenal - whose pursuit of Real Madrid's Gonzalo Higuain appears to be faltering - are preparing to offer an improvement to their £30million bid for striker Luis Suarez which was rejected last week.
Liverpool have yet to receive another approach and maintain the Uruguay international is not for sale.
The focus, meanwhile, is on bringing more players in.
"Our recruitment team are doing a great job behind the scenes in compiling lists of players that we can afford and might be available for us," said Rodgers.
"What we've done in the early part of the summer is to improve the squad. That's something I feel we've done with the players we've brought in.
"Now what's important over the next three to five weeks is improving the team. That's something the club is working very hard at.
"I'm sure by the time the end of August comes we'll be ready and we'll have a terrific squad ready to challenge."
Rodgers' new signings could all make their debuts in the Reds' first pre-season friendly at Preston on Saturday.
"There's every chance. All of the players are working here," the manager told liverpoolfc.com.
"If they are all well and fit then they will travel for the game on Saturday.
"Simon Mignolet will play, of course; Aspas, Luis Alberto and Kolo Toure - they will all get a run-out."
Having bolstered his squad with some new arrivals Rodgers is happy to allow some of the fringe players who supplemented the first-team last season to gain experience elsewhere on loan.
Press Association Sport understands young Spanish forward Suso is set to finalise a temporary deal with La Liga side Almeria while defender Andre Wisdom could also be loaned out.
However, Rodgers is keen to take the 20-year-old on the club's pre-season tour of Indonesia, Australia and Thailand and no decision is likely to be taken on his future until they return from that trip.
Midfielder Jay Spearing, who spent last season on loan at Championship club Bolton, is no nearer an exit as although Blackburn have offloaded Martin Olsson to free up some money, a deal has not progressed any further.
One player hoping to establish his place in the first team once again is Jose Enrique.
The Spaniard's future looked bleak in the first half of last season but he came good later on and he is looking to consolidate his position, which with Martin Kelly now fit could be under pressure from Glen Johnson switching sides as happened 12 months ago.
"What I want to do is play as much as I can," he said.
"I have to try to play better every season. Hopefully I can help the team, if I can score goals then much better but the most important thing for me is to help the team.
"We have a really good team; we did already last year but with the few additions we have now, we have an even better team.
"Hopefully we'll do well and get where we want to be."