Short answer: It can. The Divigel label says estradiol can pass to another person through contact with the application site, and warns about children and pets. Both labels say to wash your hands after applying and to keep others from touching the area for at least 1 hour. Divigel says to keep children away from the site and to have a child checked if signs like breast growth appear.
The Divigel label (section 5.19) says there is a potential for drug transfer from one person to another after physical contact with the application site. In its study, women applied Divigel to a thigh and then had 15 minutes of thigh-to-arm contact with a male partner, 1 and 8 hours later. Some rise in estradiol over baseline was seen in the men, but the label calls the degree of transfer inconclusive.
The EstroGel label (section 12.3) describes a study where 24 women applied EstroGel to one arm every day for 14 days, and 1 hour after each dose another postmenopausal woman held skin-to-skin contact with that arm for 15 minutes. No change in the second group's estradiol levels was seen. That was one setup, at 1 hour, between adult women; it does not cover children or contact sooner after applying.
The Divigel label (section 17) tells prescribers to inform women about unintentional secondary exposure. It says to keep children from contacting the application site, and if direct contact happens, to wash the contact area thoroughly with soap and water. It says to look for signs of unexpected sexual development in children before puberty, such as a breast lump or larger breasts, and if seen, to have the child checked by a healthcare provider and to talk to the prescriber about handling the gel around children.
The same section says pets may also be exposed if these steps are not followed. The Divigel leaflet adds that the longer the gel stays on someone else's skin before washing, the more estrogen they may absorb, and that this is especially important for men and children.
Where you apply matters for contact too: EstroGel goes on the arm and Divigel on the upper thigh. See where to apply estradiol gel and when to shower.
If a partner, child or pet has had close contact and you notice changes, write down when the contact happened, when you had applied the gel, and what you saw, and bring it to your prescriber or the child's doctor. Dose Track keeps the time of each application, which makes that timeline easy to pull up. The Divigel and EstroGel side effect pages cover each label's other warnings.
Read more on Dose Track: Divigel side effects · EstroGel side effects · Estradiol · Menopause