Talks have been held between the two clubs after the Gunners made a €7 million bid for Japanese right-back Uchida earlier this week, with Arsene Wenger sanctioning a flurry of moves for new signings.
But the straight cash offer was rejected by Schalke and a possible part-exchange deal involving Podolski has failed to get off the ground due to Wenger's reluctance to lose the Germany international.
The French boss is unwilling to sell the 28-year-old forward even though he has had a frustrating time at the Emirates Stadium since joining from Koln last year.
Podolski was omitted from the starting line-up for the Gunners’ 3-1 defeat to Aston Villa last weekend in favour of Alex Oxlade-Chamberlain but returned to the team for the 3-0 midweek win against Fenerbahce.
Goal revealed last week that Arsenal had targeted Uchida to provide defensive cover this season and be groomed as a long-term replacement for Bacary Sagna.
Wenger wants a right-back who can fit in with the Gunners’ playing style and challenge Carl Jenkinson for the first-team slot if Sagna leaves when his current agreement expires next summer.
The Frenchman re-opened contract talks with Arsenal earlier this month but there was no breakthrough and he is still expected to leave the north London club.
