The 26-year old winger was disappointing for the Galaxy after arriving at the club in May last year via a trade which saw Mike Magee head to Chicago Fire.
Arena admits Rogers was well below par in his return to soccer following a premature retirement and insists he will be on his back, as well as other attacking midfield players, in order to get the best out the talented wide man.
"I haven't given up on him," Arena said.
"It's important he play better this year. We're not going to put anyone on the field if they're not producing, if they're not playing well.
"There will be pressure on him as there will be on others. We need to push not only Robbie Rogers, but we have to push Landon (Donovan), Gyasi (Zardes), Juninho."
He added: "Robbie's had an outstanding preseason to date. I feel good about that."
Rogers himself added that 2014 is the year he needs to really make a case for himself as the Galaxy look to win back the MLS title they lost in 2013.
"I think I need to make a statement," said Rogers.
"I think our team needs to make a statement. I think, you know, we're a great team, and last year, I know it wasn't our best season, but I still felt like we could have won it."
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball