'Just promise me you will think about it, alright?'
Unbeknownst to the rest of the rankers and title holders, the current Edinburgh king was actively seeking to hire Eren as part of his personal entourage. This was an offer Emil had not extended to any Expert ranker before.
It would have been a huge honor and opportunity for the other participants. Most of them would have accepted Emil's offer immediately. The solo recipient of such honor himself had a different viewpoint on this topic.
Emil was more interested in roping Eren into his camp than making him work passively for Edinburgh. That's why he offered Eren a less-strings-attached deal.
Emil also knew that Eren wouldn't accept his offer right away because he wasn't in a hurry to do so. So he extended the offer's validity indefinitely. This was because Emil believed that Eren would soon realize what he was talking about as he progressed further in his ranking journey.