Kane, who has scored hat-tricks in consecutive games, missed training on Friday but the manager was hoping the England worldwide will still have enough time to recover.
The Tottenham striker's 37 strikes in 2017 have shunted previous holder Alan Shearer down into second place in the "most goals scored in a calendar year" stakes, with Kane's hat-trick in the 5-2 demolition of Southampton on Boxing Day writing him into the history books.
A sniffly Pochettino said: 'He is ill, a cold like me. He's at home. The doctor was there at his house.
'Will he be fit to face Swansea? "I don't know whether he will be available or not".
Fifth-placed Spurs have been able to welcome Victor Wanyama back to first-team training, however. We'll see how he reacts'.
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There have been 20 Golden Boot winners since the Premier League was founded in 1992, with three players sharing the honors in both the 1997-98 and 1998-99 seasons and two in 2010-11. Now we are assessing him. "He is not training with the group and he is another doubt for Tuesday".
"For me, there is no doubt about his quality or potential". We expect from him in every touch, every action, unbelievable things.
"From day one when he started to play at Tottenham, no young player has achieved as much. Sometimes it is not possible".
Asked about his favourite moment of 2017, Pochettino named Spurs' 2-1 win over Manchester United in the last-ever match at their old White Hart Lane home, which was followed by a farewell ceremony featuring 48 club legends.