England captain Kane's future at Tottenham has been the subject of intense speculation with the club failing to qualify for next season's Champions League.
"I'd be lying if I said I didn't (want the Premier League record), I think if I get to the end and I haven't broke that record and the Wayne Rooney England record (53 goals) then I'd probably be a little disappointed in myself," he said.
Kane hobbled off in Tottenham's 2-2 draw with Everton this month and missed Wednesday's 2-1 victory over Southampton in which Gareth Bale played up front and scored.
"We are never going to put Harry in that position, absolutely not. We will see how he is tomorrow and we can make a decision from there. Ultimately, we'll speak to him -- 'how do you feel?' -- and go from there."
Spurs came up short in the League Cup final in 2015 and the Champions League final in 2019 but Kane, 27, will have another shot at silverware when they face Manchester City at Wembley on Sunday.
"They have to (win trophies now) in terms of the stadium they have built and with the players they have got," Bournemouth manager Woodgate told British media.
"The Club can today announce that Jose Mourinho and his coaching staff Joao Sacramento, Nuno Santos, Carlos Lalin and Giovanni Cerra have been relieved of their duties," it said.
The news comes the morning after the London club said it was one of 12 clubs forming a breakaway European Super League - a development that has been widely condemned and threatens a bitter power struggle in the European game
The row erupted following Sunday's 3-1 win in the Premier League for United when Solskjaer senior criticised Spurs attacker Son Heung-min for exaggerating a blow to the face.
"I always get fed, I can assure you of that," the 20-year-old midfielder told the paper with a smile, adding that his Norwegian team mates had teased him over the incident when he arrived for training on Monday, asking if he'd had breakfast.
France international Anthony Martial was sent off in the 28th minute in the humiliating October defeat at Old Trafford after retaliating to an elbow from Erik Lamela with a push in the Argentine's face.
"We didn't look anything like (them) and we got conned into a red card and that's something we have to be aware of," Solskjaer told a news conference.
When Argentine winger Erik Lamela conjured a piece of wizardry to put Tottenham ahead against Arsenal last Sunday with a 'Rabona' goal it seemed it was rubbing off on his players.
After the most humbling European night of his glittering managerial career an ashen-faced Mourinho accused his players of failing "with the basics of life".
When the sides met at Tottenham's stadium in December goals from Son Heung-min and Harry Kane gave Spurs a 2-0 win which put them on top of the Premier League table and left Arsenal 15th.
With both sides in the last 16 of the Europa League their more likely routes to European qualification, particularly in Arsenal's case, could be by winning that competition.
"You won't see Jack at Newcastle," Smith told reporters ahead of Friday's game. "He's a lot better but it didn't help that he's been ill this week too. Very hopeful that he will be available for selection against Tottenham.
"He takes part in the meetings, he has a voice and an opinion. He's in the training ground. He's maturing an awful lot and takes on a lot of responsibility."