Learn Hardcore Greek: Μάλλον δεν έχω χρόνο αυτή την εβδομάδα.

Stronger than ίσως (“maybe/perhaps”), which is more neutral/uncertain.
Similar to μπορεί να (“it may/might”), which is also weaker than μάλλον in many contexts.

Examples:

Μάλλον θα αργήσω. = I’ll probably be late. (fairly strong)
Ίσως να αργήσω. = I might be late. (weaker)
Μπορεί να αργήσω. = I may be late. (weaker)

Where does μάλλον go in the sentence? Are other positions possible?

Most natural: put it at the beginning or right before the verb phrase.

Most common: Μάλλον δεν έχω χρόνο.
Also okay: Μάλλον αυτή την εβδομάδα δεν έχω χρόνο.
Acceptable but different emphasis: Δεν έχω μάλλον χρόνο (focus swings toward “time”).
Avoid: Δεν μάλλον έχω χρόνο (ungrammatical).

Why is it δεν and not μην?

Greek has two main negative particles:

δεν for the indicative (normal statements/questions): Δεν έχω χρόνο.
μην with the subjunctive/imperatives/after να, ας: Ίσως να μην έχω χρόνο, Να μην αργήσεις.

In your sentence we’re making a straightforward statement, so we use δεν.

Do I need the future θα here? Is Μάλλον δεν θα έχω χρόνο better?

Both are fine:

Μάλλον δεν έχω χρόνο αυτή την εβδομάδα. = A present-state statement that effectively refers to this week’s schedule; very idiomatic.
Μάλλον δεν θα έχω χρόνο αυτή την εβδομάδα. = Slightly more “future-looking” or predictive. The difference is subtle; both are natural.

Why is there no article before χρόνο? Why not τον χρόνο?

When you mean “time” in a general, non-specific, uncountable sense, Greek often uses a bare noun: (δεν) έχω χρόνο = (don’t) have time.

Έχω χρόνο; = Do I have time (in general)?
Έχω τον χρόνο; = Do I have the (specific/allocated) time? If you want to make it emphatically zero: Δεν έχω καθόλου χρόνο. (“I have no time at all.”)

What case and agreement are in αυτή την εβδομάδα?

εβδομάδα is feminine; here it’s in the accusative because time expressions commonly use the accusative.
The article agrees: την.
The demonstrative agrees: αυτή (ν) (feminine accusative singular). So: αυτή την εβδομάδα = “this week.”

Should it be αυτήν (with -ν) instead of αυτή?

Both αυτή την εβδομάδα and αυτήν την εβδομάδα are used. Many speakers drop the final -ν in everyday writing/speech. A “careful” style tends to keep the -ν before vowels and certain consonants (κ, π, τ, μπ, ντ, γκ, ξ, ψ). Since the next word here is την (starting with τ), you will also see αυτήν την εβδομάδα—but αυτή την εβδομάδα is very common and perfectly acceptable.

Why is it την εβδομάδα and not τη εβδομάδα?

The feminine accusative article appears as τη(ν). In modern usage, the -ν is kept before vowels (and often before κ, π, τ, μπ, ντ, γκ, ξ, ψ). Because εβδομάδα starts with a vowel, we write and say την εβδομάδα.

Do I need a preposition like “σε” for “this week”? Can I say σε αυτή την εβδομάδα?

No preposition is needed. Time expressions like this commonly use the bare accusative:

αυτή την εβδομάδα = this week. Using σε here sounds odd unless you mean something like “within” in a more formal phrase (e.g., μέσα σε αυτήν την εβδομάδα, “within this week”), which is a different nuance.

Can I move αυτή την εβδομάδα to a different position?

Yes. Word order is flexible for emphasis:

Αυτή την εβδομάδα μάλλον δεν έχω χρόνο. (focus on “this week”)
Μάλλον αυτή την εβδομάδα δεν έχω χρόνο. (focus slightly shifts)
Δεν έχω χρόνο αυτή την εβδομάδα. (neutral placement at the end)

How do I pronounce the sentence?

IPA: [ˈmalon ðen ˈeho ˈxɾono afˈti tin evðoˈmaða]

Tips:

μ
- ά
  - λλ
    - ο
      - ν: μάλλον = [ˈmalon] (double λ is just a single [l] sound).
δεν = [ðen] (like “th” in “this”).
έχω = [ˈeho] (χ like German “Bach,” not English “ch”).
χρόνο = [ˈxɾono] (tapped ρ).
αυτή before a voiceless consonant (τ) sounds [afˈti].
εβδομάδα = [evðoˈmaða] (ευ = ev before voiced β; δ = [ð]).

Where is the “I” in Greek? Can/should I say Εγώ?

Greek is pro‑drop: the verb ending shows the subject, so (εγώ) έχω → “I have.” You add Εγώ only for emphasis or contrast:

Εγώ μάλλον δεν έχω χρόνο αυτή την εβδομάδα, (but someone else might).

Is εβδομάδα the same as βδομάδα?

Yes, βδομάδα is a very common colloquial variant of εβδομάδα. Same meaning (“week”); εβδομάδα looks a bit more formal. Both are widely understood:

αυτή τη βδομάδα (colloquial)
αυτή την εβδομάδα (neutral/formal)

What’s the difference between χρόνος and ώρα?

χρόνος = “time” in general (also “year” in some contexts with numbers, e.g., για έναν χρόνο = “for one year”).
ώρα = “hour” or “clock time.” So Δεν έχω χρόνο = I don’t have time (generally), not “I don’t have an hour.”

How can I make the negation stronger, like “no time at all”?

Use intensifiers:

Δεν έχω καθόλου χρόνο αυτή την εβδομάδα. = I have no time at all this week.
Δεν έχω ούτε λεπτό. = I don’t have even a minute. (very emphatic)

Is there a shorter way to say “Probably not (this week)”?

Yes:

Μάλλον όχι (αυτή την εβδομάδα).
For “probably yes”: Μάλλον ναι.

Could I say Δεν προλαβαίνω instead of Δεν έχω χρόνο?

Yes, very natural:

Μάλλον δεν προλαβαίνω αυτή την εβδομάδα. = I probably won’t manage / won’t make it (timewise) this week. It focuses on not being able to fit something in, rather than the general absence of time.