Jensen has established himself as first-choice keeper at Burnley and he has previously indicated he hopes the club would offer him an improved contract as reward for his service.
The Dane's representative, Mickey Walsh, has suggested Jensen could be tempted to make a move to Portugal on a free transfer.
"He can leave on a Bosman free transfer," Walsh told the Daily Express. "He's love to play for Porto, Benfica or Sporting Lisbon."
Meanwhile, Martin Paterson, Chris McCann and Jay Rodriguez have made their long-awaited returns to action after recovering from injury.
The trio have been sidelined for close to four months with long-term injuries, but they made successful returns in Tuesday's reserve clash with Hull.
Paterson marked his return with a goal and got the full 90 minutes under his belt along with Rodriguez, while McCann featured for 70 minutes.
The news will be a boost for new Clarets boss Brian Laws as he prepares for this weekend's FA Cup clash with Reading.
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