The Hornets currently sit fourth in the table and just a point behind fellow promotion chasers Leicester and Hull City, having won four of their last five league encounters.
Italian defender Cassetti, on loan at Vicarage Road from Serie A club Udinese, says Watford are looking up.
The 35-year-old told The Independent: "Watford this year has the possibility to look up, to join the Premier League, because we have a good team and good players, young players with a great future. We know it is not easy but we can."
Cassetti is enjoying life at Watford after arriving at the beginning of the season from Udinese; also owned by Italian businessman Giampaolo Pozzo.
The defender joined the Bianconeri as a free agent when his contract at Roma expired in the summer.
"I was a free agent in June," he said. "I spoke with Pozzo, he said 'you sign for Udinese but you go on loan to Watford immediately.'
"I am happy - football in England is one of my dreams and now I am here."
Cassetti says he joked with former Roma team-mate and reported Manchester City target Daniele De Rossi over a Championship move following his row with recently-dismissed coach Zdenek Zeman at the Stadio Olimpico.
"I asked De Rossi to come here in January because of a problem with the trainer, he did not play," he added.
"When Zeman was a problem I asked him 'will you come here?' - 'I'll come!' - but Roma didn't want. But now Zeman is sacked, I think now he will start to play."