The long wait for Brendan Rodgers' fist signing since taking the reins at Liverpool could soon be over. The former Swansea boss has revealed that he hopes to have one or two players signed up to his Anfield project by the end of the week.

Rodgers was asked by Sky Sports News whether he expects to have new players on board before the club heads off on their upcoming pre-season tour of the United States.

We hope so, responded Rodgers. There certainly won't be as many as has been labeled out.

I think the reality is that for players to be associated with Liverpool is great, but the reality is that we have only made three or four enquiries about players.

Hopefully we can close out one deal this week, maybe two.

Hopefully we can do one and then look to add to it over the course of pre-season.

Rodgers has previously hinted at his frustration at having to start his recruitment drive late this summer and will be desperate to get as many deals as possible wrapped up so as to integrate signings into the club during pre-season.

One of the players targeted appears to be Real Madrid midfielder Esteban Granero. The Daily Mail reported over the weekend that Liverpool have had a big rejected for the 25-year-old former Spanish Under-21 international.

Granero made just seven starts for Real in La Liga last season, but possesses the strong passing ability that Rodgers will be keen to add to Liverpool's midfield.

The Reds could also move for Fulham's Clint Dempsey, though any deal appears to still be some way from coming to fruition.

The People reported on Sunday that Liverpool was poised to make a £6 million offer for the U.S. international. But, according to the Liverpool Echo, those claims are some way wide of the mark.

Though the local publication believes that Rodgers rates Dempsey highly as a player, it is thought that no approach has yet been made to the Cottagers.

More speculation that appears to be off track is that linking Andy Carroll with a move to Milan. After reports emerged last week suggesting the Italian giants were targeting the target man, the Sun has now claimed that the Rossoneri will make an approach to loan the England international.

In his interview with Sky Sports News, however, Rodgers appeared to quash such talk.

I haven't heard anything from [Milan] at all, he said.

He's a good player, Andy. He will always be linked whether he was here or not.

I have spoken to Andy on his holidays and he knows exactly where he stands. He's a very good young player and he will be linked with clubs like that because he's such a good player.

Another player who looks set to remain at Anfield for the foreseeable future is Craig Bellamy. Recent reports have linked the Welshman with a return to hometown club Cardiff, but Rodgers expects that the pacey forward's second spell at Liverpool will extend for a while longer.

I had a really positive chat with Craig on Monday, Rodgers said, according to ESPN.

He's a player. It would take a really special and unique opportunity for Craig to walk out of Liverpool and for us to go our separate ways.

If anything changes on that from a personal perspective then him and I will talk about that.