The Everton defender Lars Jacobsen has told David Moyes he wants to extend his brief stay at Goodison Park and provide an inexpensive solution to the Scot's search for a new right-back this summer.

Jacobsen, the Denmark international who replaced Tony Hibbert during Saturday's FA Cup final defeat to Chelsea, is out of contract this month and awaiting a decision on whether he will be offered an extension to his initial one-year deal from Moyes. The Everton manager had resolved to improve his options at right-back irrespective of Hibbert's poor display at Wembley but, with his budget limited and other areas to strengthen, he could be tempted to renew Jacobsen's terms once the defender's international commitments have ended next week.

The 29-year-old, who was restricted by a dislocated shoulder to only six appearances following his free transfer from Nuremberg, confirmed: "I hope to stay but no decision has been made yet. I have had some great months after my injury, I have come back strong and I would really love to stay here. It's been a pleasure to work with the guys. We have got a great team spirit, this is a top club, so of course I would love to stay."

Jacobsen is currently preparing for Denmark's World Cup qualifier in Sweden this weekend but may have to wait for an answer from Everton as Moyes considers alternative targets. Sheffield United's Kyle Naughton and West Ham United's Lucas Neill have been linked with Goodison, although the latter's age – he is 31 –and personal demands are unlikely to appeal to Moyes.

"I think I have done well in the games that I have played," Jacobsen added. "It was a shame that I didn't start in the Cup final but it shows that the manager has big trust in me when he put me on at half-time. Now I have a big game on Saturday with Denmark. Let's get that over and then we can talk about the other stuff like a new contract after that."