Moves to sign Jiminez, a 25-year-old midfielder and captain of Chile, are close, and now West Ham want the highly-rated Mancini.
Jiminez could arrive on loan but if West Ham want the pair on a permanent basis, they would cost in the region of £22 million.
Mancini, a Brazilian international, who has been likened to Cristiano Ronaldo by Sven-Goran Eriksson, gained a reputation as a quick and creative winger at Roma before he moved to Inter a year ago for £11m.
Mancini attracted interest from Liverpool last summer and Manchester City, who tried to sign him when Eriksson was manager.
Scott Duxbury, the West Ham chief executive, took control of the talks for Mancini and Jimenez in Milan at the weekend, alongside Gianluca Nani, the club's Italian technical director.
The move for the Inter pair highlights the influence Italian manager Gianfranco Zola is having at Upton Park.
West Ham are set to allow several players to leave and while Freddie Sears is considering several options to move out on a year's loan, Lee Bowyer is close to agreeing a pay-cut to sign for Premier League newcomers Birmingham following a successful loan spell at St Andrews last season.