Boss Arsene Wenger has given Schwarzer the extra incentive in a bid to secure the 37-year-old Fulham keeper.
Aussie Schwarzer is desperate for Champions League football and to have the chance to work with some of the club's other stoppers, along with head keeper coach Gerry Peyton.
But the Gunners must increase their bid, having seen an initial £2m offer rejected.
However, any deal will be on hold until Fulham appoint a new manager.
Wenger sees Schwarzer as a short-term fix to the club's problems.
Arsenal, who face Sturm Graz in Austria tonight, still have high hopes of 20-year-old Polish stopper Wojciech Szczesny.
Meanwhile Eduardo was in Ukraine yesterday to complete a £6m move from Arsenal to Shakhtar Donetsk.
The striker, 27, whose career in north London stalled after suffering a horrific injury at Birmingham February 2008, was not included on the 27-man list of players to travel to Arsenal's Austrian training camp this week.
Eduardo's Croatian international chief Slaven Bilic said: "I spoke with Eduardo. He was very pleased with the move to Shakhtar. He is going to a strong league.
"This season they will again play in the Champions League. This is excellent for the national team."
Shakhtar coach Mircea Lucescu said: "Yes, he had a serious injury and we are aware of the risk."