The 21-year-old arrived in the Italian capital on Wednesday and will now undergo a medical assessment at the Paideia clinic in Rome - with a deal expected to go through when his West Ham deal expires in June.
Morrison - capped at various youth levels for England - will hope to rekindle his career after spending the bulk of the last few years on loan to various second-tier clubs.
The former Manchester United man has endured off-field difficulties since leaving Old Trafford and has struggled to gain a regular spot under Sam Allardyce at Upton Park, other than a run of games at the start of last season.
Lazio sit fourth in Serie A, with Stefano Pioli's men also booking their place in the semi-finals of the Coppa Italia on Tuesday with a 1-0 win over Milan.
