LTspice Inductance simulation
I would like to vary the value of the inductance in function of the
current flowing through it.

You might be inadvertently trying to break the laws of physics.
If inductance is proportional to current (for instance) then at t = 0 (before current starts to flow) inductance must be a zero value or a short circuit. That might explain one problem you have.
Also, if inductance rises, then, to keep the energy the same at that instant (because energy just cannot appear or disappear instantaneously), current has to reduce and this creates an anomaly because then, the inductance has to fall (being proportional to current) which causes current to rise (in order to conserve the energy). That sort of situation will certainly cause problems with a simulator.
It sounds to me like you are trying to do something that is prone to difficulty.