Gunners bid for Suarez - Report
Marko Arnautovic is desperate to put a "big mistake" behind him after being offered a second chance by Werder Bremen.
Arnautovic, along with team-mate Eljero Elia, was suspended from the first team after being caught speeding in April.
He remained in exile until the end of the season but, following the summer break, has now returned to first-team training under Robin Dutt and is hoping to repay the new coach's faith in him.
"It was a great feeling to be back with the team again," he said. "I had been away for four or five weeks and that hurt.
"The issue is behind us and I'm delighted to be back. It would be stupid if I didn't learn from it.
"It was a big mistake and we know that."
Speaking from Bremen's pre-season training camp in his home country, the Austria international said he felt revitalised by talks with Dutt and the club's director of sport Thomas Eichin.
"He (Dutt) has faith in me and that is important," added Arnautovic. "I've spoken to the coach and director of sport and cleared everything up."
Eichin confirmed that Arnautovic "has apologised to Werder" and that he knows he made a mistake.
"Now he gets a fresh chance and I have told him that he starts all over again from zero," added Eichin on his club's website.
"He will be treated by me and the coaches precisely like every other player. We are a team and there are rules which Marko also has to stick to, and there are also liberties which he will be able to take like everybody else."
It is understood the Gunners made an offer in the region of £30million for the Uruguay striker last week which was rejected out of hand by the Reds.
Despite the 26-year-old this summer voicing his dislike of his treatment by the
English media and suggesting a move to Real Madrid would appeal, the club have no intention of selling, a stance which was not even tested by an offer well below what is considered Suarez's true value.
Suarez, who has three years remaining on an improved contract he signed last summer, is currently on extended leave after his involvement in the Confederations Cup.
Neither he nor his representatives have spoken to Liverpool about any intention to ask for a move but his comments while on international duty in South America have left the club in a difficult position.
It was expected any approach from Madrid would come after the end of the Confederations Cup but so far has nothing has materialised and the fear is the Spanish giants will leave it late in the window in order to drive the price down.
Arsenal's surprise bid may have been more strategic than realistic as they are currently trying to push through a deal to sign Real striker Gonzalo Higuain.
Making an offer for Suarez may have just been a ploy intended to focus the minds of Bernabeu officials on signing off the Higuain move.
Suarez is not due back for pre-season until July 22 and he will then be expected to join the club's tour matches in Australia and Thailand.