The Whites, who have just returned from a two-week pre-season training camp in northern Italy, have completed deals for goalkeepers Marco Silvestri and Stuart Taylor, midfielder Tommaso Bianchi and striker Souleymane Doukara as they prepare for the new Championship campaign.
Switzerland full-back Gaetano Berardi is expected to become Hockaday’s fifth summer addition after Sampdoria’s sports director Carlo Osti confirmed the 25-year-old would be heading to West Yorkshire, while former Newcastle striker Nile Ranger is understood to have been offered a trial.
Young Roma midfielder Federico Viviani is also the subject of interest from United, according to the 22-year-old’s agent, and although Hockaday was reluctant to give too much away, he admitted that deals are being worked on.
"There are areas where we need to strengthen and it’s not rocket science. We’re working hard to improve those areas," Hockaday told the Yorkshire Evening Post.
Ranger, meanwhile, is without a club following the mutual termination of his contract at Swindon Town at the end of last season and Sky Sports understands that Leeds have presented him with the chance to impress over the summer.
Hockaday is familiar with the controversial 23-year-old after working with him as a youth coach at Southampton between 2007 and 2008.
Leeds are known to be in the hunt to boost their attacking options after last season’s top goalscorer Ross McCormack departed for Fulham earlier this month, and Hockaday refused to rule out the possibility of taking a look at Ranger.
He said: "People are putting two and two together. There are players I’ve worked with who I keep in touch with and Nile’s one of them.
"I’m not going to pick out individuals because I could be here for a fortnight saying yes, no, yes, no, but we’re looking at a lot of players. If I get drawn into one then I’ll get drawn into others.
"Anything’s possible in football but most things aren’t going to happen. I know a lot of players and Nile’s one of them. We know where we need to strengthen.
"But we’re not going to be rushed or do anything silly. We want the right people for the right reason at the right time. If we can get it done in a day, great. If it takes a month it takes a month."