From very early on once the transfer window opened there have been stories linking Calvert-Lewin with an Everton exit.
At one point it seemed Newcastle United were close to agreeing a deal for the former England international, before that then fell through.
While this was going on, the Blues had offered the 27-year-old a new contract but so far he has refused to sign it. This does appear to indicate he at least sees his future elsewhere.
So, Everton face the prospect of losing their talisman centre-forward for nothing next summer. That would be a very significant blow. Can the club afford to risk this happening?
The context of all this is the Toffees continuing financial crisis, which has overtaken them during the last few years with rocketing debts because of so much past spending on players and managers.
All that is compounded by the continuing debacle over the club's ownership with four previous individuals or groups having been allegedly close to buying the club only for things to fall through.
Now, the Blues are waiting to see if the latest candidate - John Textor - can finally manage to conclude a deal to buy the club.
Meanwhile, the first two matches of the season both ended in heavy defeats as first Brighton and then Spurs scored a combined seven goals against the Toffees without reply, it is clear this team has major problems to be resolved.
While the unusually porus defence is probably the most obvious and pressing, a lack of goals - something that was so much a critical issues last season - also still needs resolving.
Calvert-Lewin has been integral to how Everton play for a long time now and under this current manager his importance has increased even more.
That is because Sean Dyche places such a heavy emphasis on his lone centre-forward being a physical presence, running the lines, holding the ball up and generally operating as a focal point for the team's attack.
However, while Calvert-Lewin can do all these things well, he is not a prolific goal-scorer and the Blues desperately need players who can find the back of the net.
Everton brought in two new forwards Ilman Ndiaye and Jesper Lindstrom while Jack Harrison has returned for another year's loan spell.
So far though none of them has scored in this Premier League season, although both Ndiaye and Lindstrom have had little opportunity to do so being only used as substitutes so far.
I hope that Dyche does give his new forward signings more of a chance in this coming weekend's game against Bournemouth, which has surely become a must-win match.
The other way to improve this situation and help solve the issue is to sign another striker who might be able to add more consistency in front of goal.
Of course, the problem is the Toffees are skint and are very unlikely to be able to add any more players to the squad except via loan deals.
So, the only other way would be to sell more players and use that money to strengthen key positions.
Selling Calvert-Lewin would be a big call for the club given that none of the other strikers on the books - Beto, Yousef Chermiti and Neal Maupay - are prolific either.
Furthermore, Chermiti is injured long-term and Maupay is probably going to leave as he clearly has no place in Dyche's plans.
Now comes a new transfer rumour that Calvert-Lewin could very well leave by Friday's deadline day with Chelsea the new favourites for his signature.
In return for his departure, this report claims that Everton will get Armando Broja in return, although it is not clear if it would be a direct swap deal.
Broja was it seemed in his way to Ipswich Town - who beat the Blues to another player they wanted to sign: Kalvin Phllips - before this move broke down.
Would bringing Broja in represent an improvement in Calvert-Lewin's goal threat? Looking at his recent statistics the answer is no.
Finding a productive and consistently reliable goal-scorer is the most challenging on-the-pitch problem that any club has to wrestle with.
For a team in Everton's position with severe financial restrictions and a poor side struggling already this season, that problem is even harder to resolve.
Will Calvert-Lewin go by the end of the transfer window? It is impossible to know for sure, but it does look as though these stories will continue right up to the deadline on Friday night.