The French midfielder has joined the Serie C side on loan until the end of the season, despite the Blues making contact with parent club Torino over a similar move.
Pompey were keen to add the 20-year-old to their ranks for the remainder of the campaign.
Boss Kenny Jackett has already reinforced his midfield this month with the loan signings of Harvey White (Spurs) and George Byers (Swansea), but still wanted Adopo on the south coast to take a closer look at him ahead of a possible permanent deal in the summer.
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The former French under-18 international would not have counted towards the 22-man squad limit all League One side’s now operate under, which would have allowed the move to happen.
However, Pompey’s interest was always in danger of collapsing following the UK’s recent departure from the European Union and newly-introduced Brexit laws.
From January 1, all English clubs have new regulations they must adhere to when it comes to recruiting players from abroad.
Potential foreign signings will now need a visa to work and live in the UK or a governing body endorsement (GBE) – a points-based qualification which has been agreed upon by the FA, the EFL and Premier League – and given Home Office approval.
It was always likely such requirements would scupper any move for Adopo, allowing Viterbese to steal a march on the Blues.
Viterbese are currently 15th in the Serie C Group C standings.
Jackett hasn’t ruled out further signings between now and the January transfer deadline, which is 11pm on Monday.
The Blues’ acquisition of keeper Lewis Ward on loan on Thursday means they have reached the 22-man ceiling permitted.
Any new arrivals, though, are likely to be aged under-21.