Sky Italia have claimed Inter Milan have contacted Bolton over the striker's availability, and the Wanderers response was to slap a €10million (approx £8.4million) on Elmander's head.
The Swedish international is out of contract in June and there have been widespread reports Bolton could cash in on Elmander in January, with Liverpool heavily linked with a £5million move.
However, the reports in Italy suggest Bolton are willing to allow Elmander's contract to run down rather than lose him in January, with the club well placed to fight for a spot in Europe.
Recent financial results show Bolton are heavily in debt, but the majority of the debt is to owner Eddie Davies and boss Owen Coyle has stated he is under no pressure to sell in January.
The Wanderers are believed to have offered Elmander a 12-month contract extension in a bid to retain his services, although so far no deal has been reached.
Elmander has pledged to focus his efforts on Bolton until his contract comes to an end, with the striker suggesting he would like a longer contract than the 12-month extension he has been offered.
"Of course, as a footballer, you like to have a big contract, but I don't want to comment on negotiations," he told the Scottis Sun.
"I will give myself fully to Bolton while I am here and when my contract runs out in the summer, we'll see what happens.
"I have never been a player who goes after money, I have always chosen with my heart and the feeling I have in the pit of my stomach."
A number of clubs have been linked with Elmander after his sparkling form over the course of the season so far, with Everton, Stoke, Spartak Moscow and Fenerbahce all credited with an interest.