Gareth Southgate remains hopeful of convincing Mark Viduka and Jonathan Woodgate that their futures lie at Middlesbrough.
Viduka's contract expires at the end of the season and Southgate fears he may be tempted to leave to embark on a new challenge.
But the Boro boss insists every effort is being made to persuade the Australian to stay on Teesside.
"We've had discussions with Mark and with his representatives and he obviously wants time to have a think about things," Southgate told the club's official website.
"I'm sure he'll have other options available to him, not just here but across Europe.
"He has to think about those things and I respect that.
"He's been a very important player to us this season and we've left him in no uncertain terms that we'd love him to be here next year."
Woodgate's future will also be resolved over the next couple of months, with the defender currently on a season-long loan from Real Madrid.
Southgate believes the odds could be in Boro's favour, as Woodgate has enjoyed an injury-free year with Middlesbrough and earned an England recall.
"Jonathan is different because he's not our player at the moment and Mark is," Southgate explained.
"There are lots of positives for him. He's broken back into the England squad while playing with us, so we've shown his international ambitions won't be harmed by being here.
"It's a big decision for Jonathan to make. The fact that he's enjoyed the season as much as he has is in our favour, but he's with a big club and he has to decide what he wants to do."