Monophthongization (of diphthongs in Latin) most likely happened after Osthoff's shortening (in Proto-Italic).
Osthoff's law: A long vowel before a liquid, nasal, or glide plus a stop was shortened (Weiss 2009, p. 125).
Monophthongization in this case was *eu > *ū (completed by the end of the 3rd century BCE),
/eu/ > /ou/ > /o̝ː/ > /uː/ (Clackson and Horrocks 2007/2011: 95).
Note that Osthoff's shortening most likely happened already in Proto-Italic, cf. Meiser 1998 "Schon im Uritalischen
sind Langdiphthonge vor Konsonant gekürzt worden" (p. 75) or Sihler 1995 "[l]ong vowels were shortened in prehistoric times before a resonant plus consonant" (para 82).
*nouentiio > nountios (G.L. 6.12.18; Tronskii 1960: 104) > nuntius (*neu- 'shout') (Weiss 2009: 278).
However, Weiss 2009 writes that Osthoff's law happened "at least three times in the history of Latin" (p. 125).
Weiss does mention that "probably yet another round of Osthoff's also applied after monophthongization (P. 126) and he gives one example,
*oino(m)-dekem > ūndecim > undecim
Note the word "probably" though; cf. Leumann, Hofmann, and Szantyr 1977, para 119:γ, "Verhältnismäßig jung (frühestens IIa) muss die Kürzung erfolgt sein bei ī und ū aus oi ou ove."
That is why - taking into account evidence from ancient grammars and Romance languages - Sihler 1995 writes that "[e]vidence for the length of these vowels, however, is conflicting (para 82b).
NB: Sihler reasonably avoids referring to vowel shortening in Greek and Latin as Osthoff's Law because these two processes were independent (i.e. not shared innovations).