Purported Liverpool target Nikica Jelavic has been urged to stay at Rangers, after the Croatian scored twice in the win over St Johnstone at the weekend.
Jelavic, 26, has been heavily linked with a move to Merseyside in the wake of Luis Suarez's eight-match ban for racially abusing Manchester United's Patrice Evra.
Manager Ally McCoist last week refuted claims the club had received an offer for the striker after the player admitted he was hugely flattered by the alleged interest from Liverpool.
Jelavic took his season's tally to 14 goals in 21 appearances in the 2-1 win at McDiarmid Park and stand-in captain Davis said he remained hopeful the club would reject any formal interest from Liverpool.
"The good thing about Jela is that he can score a mixture of goals and he got two poacher's goals in this game," Davis is quoted in the Daily Telegraph.
"He showed he's got a desire to still do well for Rangers so, hopefully, the club can keep hold of him.
"There has been a lot written in the press saying he wants to move on but he always works hard for the team and it was good to see him get his rewards again for the effort he puts in."
Earlier this month, Jelavic acknowledged his head had been turned by Liverpool's reported interest but said he was yet to hear from any other clubs.
In addition to interest from Liverpool, Dalglish's Premier League rivals West Brom, Sunderland and Everton have all been associated with the striker.
"Every day it appears a new club wants me and that's a little ridiculous," the reputed Liverpool target told the Daily Mail. "I know nothing about any offers. I just want to concentrate on Rangers.
"I have another two-and-a-half years left of my contract but, if the club decides to sell me, because I know that we are in a difficult financial situation, then fine.
"Of course I am flattered about Liverpool, but I do not know how much truth there is," he added. "Therefore, I don't pay attention because I do not want to create additional pressure.
"My job is to play. Liverpool is a great name but, like I say, the question is how much are they really interested?"
Jelavic has hit a remarkable 30 goals in 40 league appearances for Rangers since moving from Rapid Vienna in August 2010.