Bougherra played for Algeria against England in their goaless draw during the group stages of the World Cup in Cape Town and his performance further increased his growing reputation.
The 27-year-old has spent the past two seasons with Rangers, helping them win the Scottish Premier League title from Old Firm rivals Celtic.
However, the former Sheffield Wednesday and Charlton defender admits a move south of the border is appealing, with both Liverpool and Arsenal reported to be interested.
"First of all I am a Rangers player, my contract runs until 2012, so I am fine there," Bougherra told Sky Sports' website.
"I heard that Hamburg and Arsenal are interested through the papers, but there is nothing official as yet.
"I am tired after the World Cup, so I want to have a holiday and recharge for next season."
Bougherra, who joined Rangers for £2.5million during January 2007, added: "I would choose the Premier League if I had a choice, I love the English mentality and their football is the best.
"I want to test myself against the likes of (Wayne) Rooney, (Didier) Drogba, (Fernando) Torres and (Emmanuel) Adebayor as those guys let you know what level you are at.
"For me, it is also time for pay back because I don't think a lot of people remember that I played in the Premier League with Charlton."