By using the Löwenheim–Skolem theorem & Mostowski collapse, in every model $V$ of $ZF$ there is a countable transitive set $M$ such that $(M,\in_M) \models ZF$. Is the following "converse" true?

In every model $V$ of $ZF$ and every transitive set $M \in V$ such that $(M,\in_M) \models ZF$, there exists a transitive set $N \in V$ such that:

1. $M \subseteq N$

2. $(N,\in_N) \models ZF$

3. $M$ is countable inside $N$

By using the Löwenheim–Skolem theorem & Mostowski collapse, in every model $V$ of $ZF+Con(ZF)$ there is a countable transitive set $M$ such that $(M,\in_M) \models ZF$. Is the following "converse" true?

In every model $V$ of $ZF$ and every transitive set $M \in V$ such that $(M,\in_M) \models ZF$, there exists a transitive set $N \in V$ such that:

1. $M \in N$

2. $(N,\in_N) \models ZF$

3. $M$ is countable inside $N$