US striker Clint Dempsey had been keen to make the jump to Anfield, but Liverpool left it late to show interest. The Fulham player moved to Tottenham Hotspur.
Yossi Benayoun was also one of the names being fired around, with speculation the Israeli star could be on his way back to Anfield from Chelsea.
However, he instead returned on loan to another former club - West Ham.
The transfer window closed at 11pm on Friday.
Carnlough man Rodgers earlier told reporters his objective was to bring in proven goalscorers.
"We're hopeful," Rodgers said, during a press conference ahead of his side's game against Arsenal.
"There are obviously a lot of people upstairs who are doing a lot of great work and working very, very hard. Let's hope by the time it shuts later on that we've got some reinforcements."
If we can get recognised goalscorers to come in, that's the objective.
Rodgers confirmed that there had still been a number of players who were the subject of enquiries and that he had been looking to make one or maybe two signings.
"Lots of names that have been thrown out there, unfortunately, have been thrown out there for other reasons than us having the money and resources to get them in, which is the brutal honesty of it," he added.
The Carnlough man has already explained letting striker Andy Carroll go because he couldn't afford to keep a £35m player as a third choice.
"He wants game time. He's a good guy, has worked well in training, but I can only pick 11 players and I've got some wonderful talents here like Luis Suarez," Rodgers said.
Charlie Adam, who has left Liverpool in a £5m deal with Stoke City, said: "The opportunity to play was getting less and I felt that, at my age, I wanted to play every week and hopefully I'll get a chance to here."
"It's a great club that's going in the right direction - the foundations are here."
Among the other outward traffic from Anfield, Jay Spearing has been loaned out to Owen Coyle's Bolton Wanderers for the season.
I don't want to, out of respect for the other clubs and players, sit and go through every single name that has been linked with Liverpool.
Making the move to Liverpool is German youth striker Samed Yesil, signed from Bayer Leverkusen.
Rodgers, who has previously stated his intentions to introduce stability at Anfield and build a club for the future, is keen to develop younger players and has high hopes for Yesil.
"He had a terrific tournament at the U17 World Cup and we hope that over the next couple of years, we'll see how he comes along," the manager said.
"He's a goalscorer, he comes in with good pedigree and I hope we can see him develop and progress through to the first team."
Meanwhile, after guiding Liverpool to the group stages of the Europa League, Rodgers now knows who his side will face - with the Reds first out of the pot in Friday's draw.
The draw took place in Monaco and saw Liverpool - one of the 12 top seeds - picked for Group A, alongside Italy's Serie A side Udinese, Switzerland's Young Boys and FC Anzhi Makhachkala of Russia.
Newcastle have been drawn in Group D, joined by Bordeaux, Club Brugge and Marítimo.
Tottenham will play in Group J, where they're joined by Panathinaikos, Lazio and Maribor.