The Borussia Dortmund striker's move to Bayern Munich at the end of the season on a free transfer was confirmed earlier in January.
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"Lewandowski has been my friend for a very long time," he told Arsenal Player after the victory over Fulham.
When asked if he was unable to convince Lewandowski to join, he added: "I tried my best [to get him to join Arsenal]."
Szczesny was quick to praise Santi Cazorla after the midfield playmaker scored both goals in the 2-0 win against Fulham on Saturday.
"I think Santi's always been a very important player for us and when he plays like he did [against Fulham] he's one of the best in the Premier League," Szczesny said.
"We're very happy to have him and delighted for him because he's not scored a lot of goals and he was getting a bit frustrated so this will be a very enjoyable game for him."