Ever since the summer transfer window opened, it has been crystal clear that the number one priority is signing a genuine goal-scorer who can add the firepower that Everton's side have clearly lacked for so long.
In addition, it has also been very likely that the club's former number one choice up front Dominic Calvert-Lewin, will leave at the end of this month, forcing transfer activity anyway.
After failing to persuade Liam Delap to choose Merseyside and seeing him decide on Chelsea instead, the Toffees were forced to consider other options.
One name that surprisingly emerged was Mitrovic, with reports circulating that the Blues were considering bringing the former Fulham player back to the Premier League.
The Serbian international has a strong track record of scoring goals wherever he has played, including in English football with the Cottagers, where he showed he was a genuine Premier League-level centre-forward.
However, the combination of his being over 30 and the sort of fee being mentioned for any transfer from his Saudi League club to Everton represented major stumbling blocks.
Since making the big money move to the Middle East, the Serbian star has still been prolific, both in domestic football and with the national team.
But it remains an open question if Mitrovic could continue to replicate the sort of productivity he has previously shown were he to return to England and a league that is certainly much better than the one he is playing in at the moment.
It does appear that the first-choice striker that Moyes would like to sign is still Villarreal's French starlet Thierno Barry.
The problem is that Barry's club are in a strong position with the Spanish side entering Europe next season and a likely competition for the forward's signature were they to decide to sell.
Furthermore, his release clause is around £35 million, and given all of the above, Villarreal can drive a hard bargain on this price.
Therefore, Mitrovic's name might well come back into the picture in a serious way, as it looks as though he is available and wants a move back to the Premier League.
And, while it is the biggest single question, solving this striker issue is just one of a number of pressing player problems facing Everton as the club and its new owners seek to position the team to become much more competitive next season.