I did a quick search and found the following:
Barrick et al (2005) (see Table 1). In a sample with a little over a hundred MBA students they obtained the following correlations with self-monitoring:
- Conscientiousness r = -.24
- Extraversion r = .31
- Agreeableness r = -.08
- Emotional Stability r = -.10
- Openness r = .23
Kring, Smith, and Neale (1994) (see Table 3): Correlations with self-monitoring were (I think in a sample of 300+ undergraduates):
- Surgency (somewhat similar to extraversion): .51
- Agreeableness: r = .06
- Conscientiousness: r = -.15
- Emotional Stability: r = .37
This would suggest that self-monitoring has only a weak relationship with the Big 5.
The positive relationship with extraversion makes sense given that self-monitoring is related to an aptitude and an interest in adaptive social interactions.
- Barrick, M. R., Parks, L., & Mount, M. K. (2005). Self‐monitoring as a moderator of the relationships between personality traits and performance. Personnel Psychology, 58(3), 745-767.
- Kring, A. M., Smith, D. A., & Neale, J. M. (1994). Individual differences in dispositional expressiveness: development and validation of the Emotional Expressivity Scale. Journal of personality and social psychology, 66(5), 934.