Manager Craig Levein will "keep plugging away" in a bid to extend Steven Naismith's stay at Hearts.
The 32-year-old Scotland forward will be a free agent in the summer when his second loan deal from Norwich expires.
Midfielder Arnaud Djoum, 27, will also be out of contract at the end of May and Levein confirmed that offers have been made to retain both men.
"It would be good to get all the ones signed up who give us that stability I keep talking about," he said.
Djoum moved to Tynecastle from Lech Poznan in 2015 but the Edinburgh club may struggle to meet the Cameroon international's demands.
"I want Arnaud to stay but he said to me a while ago that if something comes up that at his age is worth an awful lot of money, then he would probably look to take it," said Levein.
"But he likes it here in Edinburgh and his family are settled. There is more to life than money."
Naismith has scored 13 goals in 22 outings for Hearts this season and that good form has earned him an international recall.
The former Kilmarnock, Rangers and Everton player said last month that his time at Tynecastle has been "fantastic" but stressed that he would take time to consider his future.
"I believe Steven is happy here but again it depends on whether something else comes up in the next couple of months that piques his interest," said Levein. "But I'll keep plugging away."
Christophe Berra, John Souttar and Michael Smith have all agreed new deals in recent weeks, with Levein saying: "My strike rate isn't bad so far, so I'll just need to keep it going."
Levein revealed that Uche Ikpeazu has returned to full training and will take some part in Sunday's Scottish Cup tie against Auchinleck Talbot.
The 23-year-old striker scored four goals in 10 appearances before he needed foot surgery for an injury sustained in mid-October.
"Uche trained with the group yesterday," said Levein. "He will definitely be involved on Sunday. Tomorrow [at home to Livingston] might come just a little bit too early.
"He has worked ever so hard and it was the same in the summer when he arrived. His energy and enthusiasm is evident for all to see. We didn't just miss his goals and his hold-up play, it was that raw energy and enthusiasm than can unsettle the opposition."