Probably not … but perhaps genes that predispose to certain personality or cognitive traits that help/hinder our ability to form stable social bonds.
“Several demographic variables including marriage, having siblings and children and educational attainment explain part of the variance in loneliness. Genetic factors, both additive and non-additive, explain about 37% of the variance.”
Genes 2 Brains 2 Mind 2 Me 
[…] Are there loneliness genes? (genes2brains2mind2me.com) […]