Mascherano is being link with Inter Milan, where he would be reunited with Rafael Benitez, and has admitted to taking Italian lessons. But Hodgson believes the Argentina international will remain at Anfield.
Hodgson has placed a call to Mascherano, but has not heard anything back.
"He doesn't need to make contact with me,'' said Hodgson. "I've made contact with him telling him I'm looking forward to seeing him in training when he returns from his holiday but I did make the point in the voicemail that I didn't expect him to contact me.
"I just wanted him to know that I had been in touch and that I was thinking of him. I didn't ask him to call me back. I don't have a lot to say to him, to be honest, other than 'welcome back'.''
Meanwhile, with defender Emiliano Insua's transfer to Fiorentina nearing completion Hodgson is keen to find a replacement as soon as possible.
"We are short and that is going to be one of the priorities,'' added Hodgson. "We need to find a replacement for Emiliano and Fabio Aurelio. That is one job we will have to do. As far as we understand, the deal (for Insua) has been completed between the clubs and his agent is sorting out personal terms. Maybe it was the right time for him to move on.''
New signing Jonjo Shelvey, who moved to Liverpool from Charlton in May, has set himself a target of making at least 20 appearances for Liverpool next season - although he admits the prospect of playing for the Reds in the Premier League still has not fully sunk in.
"Being at Liverpool is what every kid dreams of,'' Shelvey told the club's official website. "When I was in school and in the playground I used to pretend to be players like Steven Gerrard, so it's unreal to think I'll be training with these players day in and day out.
"I'm really excited and can't wait for the season to start now. I want to get at least 20 games under my belt this season so I can start getting myself into it. I am confident, you have to be. When you are 18 years of age and you are getting thrown into games at Anfield then you can't have any fear. You have to go and do what you do.
"Obviously it's a different lifestyle compared to being at Charlton. The training is harder, everyone is a top quality professional, so it's totally different. It's different but I'm enjoying it. It's hard but I'm coping with it and it's good to be here. It still hasn't really sunk in now that I could be playing in the Premier League week in and week out. It's unreal.
"I'm an all-action player. I can defend, although I'd rather be bombing on to score goals and create things. I used to play in the hole behind the striker at Charlton but I prefer to play in central midfield to dictate the play.
"From watching the Premier League on the television you seem to get a lot more time and space on the ball compared to League One and that will suit me. I just can't wait to show the fans what I can do.''