Difficult to tell with some players, for most at this stage of their career it's a cash grab. Majority would rather have well paid long term deal rather less money on the off chance of securing major honours.
In Alexis' case I doubt he'll see successive Bundesliga titles as worth the pay cut. If his urge to win the CL was that strong he would have probably stayed at Barca tbh. He knew what level he was dropping down to when he joined. Arsenal will most likely offer him a £200K+ 5 year deal whereas Bayern, for someone who will be 29 in December, will offer £120K if he's lucky on a 3 year deal along with no guarantee of starting or tactical freedom.
It's all speculation but bare it mind only a few months ago Alexis indicated that he was happy to sign if the club 'show confidence' in him. Arsenal's competitive issues weren't an issue for him then